We show, by an explicit construction, that a mixture of univariate Gaussians with variance 1 and means in $[-A,A]$ can have $Omega(A^2)$ modes. This disproves a recent conjecture of Dytso, Yagli, Poor and Shamai [IEEE Trans. Inform. Theory, Apr. 2020], who showed that such a mixture can have at most $O(A^2)$ modes and surmised that the upper bound could be improved to $O(A)$. Our result holds even if an additional variance constraint is imposed on the mixing distribution. Extending the result to higher dimensions, we exhibit a mixture of Gaussians in $mathbb{R}^d$, with identity covariances and means inside $[-A,A]^d$, that has $Omega(A^{2d})$ modes.

This paper is devoted to investigate whether the popular No U-turn (NUTS) sampling algorithm is correct, i.e. whether the target probability distribution is emph{exactly} conserved by the algorithm. It turns out that one of the Gibbs substeps used in the algorithm cannot always be guaranteed to be correct.

Data-space inversion (DSI) and related procedures represent a family of methods applicable for data assimilation in subsurface flow settings. These methods differ from model-based techniques in that they provide only posterior predictions for quantities (time series) of interest, not posterior models with calibrated parameters. DSI methods require a large number of flow simulations to first be performed on prior geological realizations. Given observed data, posterior predictions can then be generated directly. DSI operates in a Bayesian setting and provides posterior samples of the data vector. In this work we develop and evaluate a new approach for data parameterization in DSI. Parameterization reduces the number of variables to determine in the inversion, and it maintains the physical character of the data variables. The new parameterization uses a recurrent autoencoder (RAE) for dimension reduction, and a long-short-term memory (LSTM) network to represent flow-rate time series. The RAE-based parameterization is combined with an ensemble smoother with multiple data assimilation (ESMDA) for posterior generation. Results are presented for two- and three-phase flow in a 2D channelized system and a 3D multi-Gaussian model. The RAE procedure, along with existing DSI treatments, are assessed through comparison to reference rejection sampling (RS) results. The new DSI methodology is shown to consistently outperform existing approaches, in terms of statistical agreement with RS results. The method is also shown to accurately capture derived quantities, which are computed from variables considered directly in DSI. This requires correlation and covariance between variables to be properly captured, and accuracy in these relationships is demonstrated. The RAE-based parameterization developed here is clearly useful in DSI, and it may also find application in other subsurface flow problems.

The very first case of corona-virus illness was recorded on 30 January 2020, in India and the number of infected cases, including the death toll, continues to rise. In this paper, we present short-term forecasts of COVID-19 for 28 Indian states and five union territories using real-time data from 30 January to 21 April 2020. Applying Holt's second-order exponential smoothing method and autoregressive integrated moving average (ARIMA) model, we generate 10-day ahead forecasts of the likely number of infected cases and deaths in India for 22 April to 1 May 2020. Our results show that the number of cumulative cases in India will rise to 36335.63 [PI 95% (30884.56, 42918.87)], concurrently the number of deaths may increase to 1099.38 [PI 95% (959.77, 1553.76)] by 1 May 2020. Further, we have divided the country into severity zones based on the cumulative cases. According to this analysis, Maharashtra is likely to be the most affected states with around 9787.24 [PI 95% (6949.81, 13757.06)] cumulative cases by 1 May 2020. However, Kerala and Karnataka are likely to shift from the red zone (i.e. highly affected) to the lesser affected region. On the other hand, Gujarat and Madhya Pradesh will move to the red zone. These results mark the states where lockdown by 3 May 2020, can be loosened.

In this paper we propose a bimodal gamma distribution using a quadratic transformation based on the alpha-skew-normal model. We discuss several properties of this distribution such as mean, variance, moments, hazard rate and entropy measures. Further, we propose a new regression model with censored data based on the bimodal gamma distribution. This regression model can be very useful to the analysis of real data and could give more realistic fits than other special regression models. Monte Carlo simulations were performed to check the bias in the maximum likelihood estimation. The proposed models are applied to two real data sets found in literature.

Segmentation of cardiac images, particularly late gadolinium-enhanced magnetic resonance imaging (LGE-MRI) widely used for visualizing diseased cardiac structures, is a crucial first step for clinical diagnosis and treatment. However, direct segmentation of LGE-MRIs is challenging due to its attenuated contrast. Since most clinical studies have relied on manual and labor-intensive approaches, automatic methods are of high interest, particularly optimized machine learning approaches. To address this, we organized the "2018 Left Atrium Segmentation Challenge" using 154 3D LGE-MRIs, currently the world's largest cardiac LGE-MRI dataset, and associated labels of the left atrium segmented by three medical experts, ultimately attracting the participation of 27 international teams. In this paper, extensive analysis of the submitted algorithms using technical and biological metrics was performed by undergoing subgroup analysis and conducting hyper-parameter analysis, offering an overall picture of the major design choices of convolutional neural networks (CNNs) and practical considerations for achieving state-of-the-art left atrium segmentation. Results show the top method achieved a dice score of 93.2% and a mean surface to a surface distance of 0.7 mm, significantly outperforming prior state-of-the-art. Particularly, our analysis demonstrated that double, sequentially used CNNs, in which a first CNN is used for automatic region-of-interest localization and a subsequent CNN is used for refined regional segmentation, achieved far superior results than traditional methods and pipelines containing single CNNs. This large-scale benchmarking study makes a significant step towards much-improved segmentation methods for cardiac LGE-MRIs, and will serve as an important benchmark for evaluating and comparing the future works in the field.

Official counts of COVID-19 deaths have been criticized for potentially including people who did not die of COVID-19 but merely died with COVID-19. I address that critique by fitting a generalized additive model to weekly counts of all registered deaths in England and Wales during the 2010s. The model produces baseline rates of death registrations expected in the absence of the COVID-19 pandemic, and comparing those baselines to recent counts of registered deaths exposes the emergence of excess deaths late in March 2020. Among adults aged 45+, about 38,700 excess deaths were registered in the 5 weeks comprising 21 March through 24 April (612 $pm$ 416 from 21$-$27 March, 5675 $pm$ 439 from 28 March through 3 April, then 9183 $pm$ 468, 12,712 $pm$ 589, and 10,511 $pm$ 567 in April's next 3 weeks). Both the Office for National Statistics's respective count of 26,891 death certificates which mention COVID-19, and the Department of Health and Social Care's hospital-focused count of 21,222 deaths, are appreciably less, implying that their counting methods have underestimated rather than overestimated the pandemic's true death toll. If underreporting rates have held steady, about 45,900 direct and indirect COVID-19 deaths might have been registered by April's end but not yet publicly reported in full.

In the Gaussian sequence model $Y= heta_0 + varepsilon$ in $mathbb{R}^n$, we study the fundamental limit of approximating the signal $ heta_0$ by a class $Theta(d,d_0,k)$ of (generalized) splines with free knots. Here $d$ is the degree of the spline, $d_0$ is the order of differentiability at each inner knot, and $k$ is the maximal number of pieces. We show that, given any integer $dgeq 0$ and $d_0in{-1,0,ldots,d-1}$, the minimax rate of estimation over $Theta(d,d_0,k)$ exhibits the following phase transition: egin{equation*} egin{aligned} inf_{widetilde{ heta}}sup_{ hetainTheta(d,d_0, k)}mathbb{E}_ heta|widetilde{ heta} - heta|^2 asymp_d egin{cases} kloglog(16n/k), & 2leq kleq k_0,\ klog(en/k), & k geq k_0+1. end{cases} end{aligned} end{equation*} The transition boundary $k_0$, which takes the form $lfloor{(d+1)/(d-d_0) floor} + 1$, demonstrates the critical role of the regularity parameter $d_0$ in the separation between a faster $log log(16n)$ and a slower $log(en)$ rate. We further show that, once encouraging an additional '$d$-monotonicity' shape constraint (including monotonicity for $d = 0$ and convexity for $d=1$), the above phase transition is eliminated and the faster $kloglog(16n/k)$ rate can be achieved for all $k$. These results provide theoretical support for developing $ell_0$-penalized (shape-constrained) spline regression procedures as useful alternatives to $ell_1$- and $ell_2$-penalized ones.

Cooperation between different data owners may lead to an improvement in forecast quality - for instance by benefiting from spatial-temporal dependencies in geographically distributed time series. Due to business competitive factors and personal data protection questions, said data owners might be unwilling to share their data, which increases the interest in collaborative privacy-preserving forecasting. This paper analyses the state-of-the-art and unveils several shortcomings of existing methods in guaranteeing data privacy when employing Vector Autoregressive (VAR) models. The paper also provides mathematical proofs and numerical analysis to evaluate existing privacy-preserving methods, dividing them into three groups: data transformation, secure multi-party computations, and decomposition methods. The analysis shows that state-of-the-art techniques have limitations in preserving data privacy, such as a trade-off between privacy and forecasting accuracy, while the original data in iterative model fitting processes, in which intermediate results are shared, can be inferred after some iterations.

Datasets in sleep science present challenges for machine learning algorithms due to differences in recording setups across clinics. We investigate two deep transfer learning strategies for overcoming the channel mismatch problem for cases where two datasets do not contain exactly the same setup leading to degraded performance in single-EEG models. Specifically, we train a baseline model on multivariate polysomnography data and subsequently replace the first two layers to prepare the architecture for single-channel electroencephalography data. Using a fine-tuning strategy, our model yields similar performance to the baseline model (F1=0.682 and F1=0.694, respectively), and was significantly better than a comparable single-channel model. Our results are promising for researchers working with small databases who wish to use deep learning models pre-trained on larger databases.

Spatial trajectories are ubiquitous and complex signals. Their analysis is crucial in many research fields, from urban planning to neuroscience. Several approaches have been proposed to cluster trajectories. They rely on hand-crafted features, which struggle to capture the spatio-temporal complexity of the signal, or on Artificial Neural Networks (ANNs) which can be more efficient but less interpretable. In this paper we present a novel ANN architecture designed to capture the spatio-temporal patterns characteristic of a set of trajectories, while taking into account the demographics of the navigators. Hence, our model extracts markers linked to both behaviour and demographics. We propose a composite signal analyser (CompSNN) combining three simple ANN modules. Each of these modules uses different signal representations of the trajectory while remaining interpretable. Our CompSNN performs significantly better than its modules taken in isolation and allows to visualise which parts of the signal were most useful to discriminate the trajectories.

In recent years, multi-access edge computing (MEC) is a key enabler for handling the massive expansion of Internet of Things (IoT) applications and services. However, energy consumption of a MEC network depends on volatile tasks that induces risk for energy demand estimations. As an energy supplier, a microgrid can facilitate seamless energy supply. However, the risk associated with energy supply is also increased due to unpredictable energy generation from renewable and non-renewable sources. Especially, the risk of energy shortfall is involved with uncertainties in both energy consumption and generation. In this paper, we study a risk-aware energy scheduling problem for a microgrid-powered MEC network. First, we formulate an optimization problem considering the conditional value-at-risk (CVaR) measurement for both energy consumption and generation, where the objective is to minimize the loss of energy shortfall of the MEC networks and we show this problem is an NP-hard problem. Second, we analyze our formulated problem using a multi-agent stochastic game that ensures the joint policy Nash equilibrium, and show the convergence of the proposed model. Third, we derive the solution by applying a multi-agent deep reinforcement learning (MADRL)-based asynchronous advantage actor-critic (A3C) algorithm with shared neural networks. This method mitigates the curse of dimensionality of the state space and chooses the best policy among the agents for the proposed problem. Finally, the experimental results establish a significant performance gain by considering CVaR for high accuracy energy scheduling of the proposed model than both the single and random agent models.

Multi-Class Incremental Learning (MCIL) aims to learn new concepts by incrementally updating a model trained on previous concepts. However, there is an inherent trade-off to effectively learning new concepts without catastrophic forgetting of previous ones. To alleviate this issue, it has been proposed to keep around a few examples of the previous concepts but the effectiveness of this approach heavily depends on the representativeness of these examples. This paper proposes a novel and automatic framework we call mnemonics, where we parameterize exemplars and make them optimizable in an end-to-end manner. We train the framework through bilevel optimizations, i.e., model-level and exemplar-level. We conduct extensive experiments on three MCIL benchmarks, CIFAR-100, ImageNet-Subset and ImageNet, and show that using mnemonics exemplars can surpass the state-of-the-art by a large margin. Interestingly and quite intriguingly, the mnemonics exemplars tend to be on the boundaries between different classes.

We study the information content of nuclear masses from the perspective of global models of nuclear binding energies. To this end, we employ a number of statistical methods and diagnostic tools, including Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis, and empirical coverage probability. Using a Bayesian framework, we investigate the structure of the 4-parameter Liquid Drop Model by considering discrepant mass domains for calibration. We then use the chi-square correlation framework to analyze the 14-parameter Skyrme energy density functional calibrated using homogeneous and heterogeneous datasets. We show that a quite dramatic parameter reduction can be achieved in both cases. The advantage of Bayesian model averaging for improving uncertainty quantification is demonstrated. The statistical approaches used are pedagogically described; in this context this work can serve as a guide for future applications.

Beginning from a basic neural-network architecture, we test the potential benefits offered by a range of advanced techniques for machine learning, in particular deep learning, in the context of a typical classification problem encountered in the domain of high-energy physics, using a well-studied dataset: the 2014 Higgs ML Kaggle dataset. The advantages are evaluated in terms of both performance metrics and the time required to train and apply the resulting models. Techniques examined include domain-specific data-augmentation, learning rate and momentum scheduling, (advanced) ensembling in both model-space and weight-space, and alternative architectures and connection methods.

Following the investigation, we arrive at a model which achieves equal performance to the winning solution of the original Kaggle challenge, whilst being significantly quicker to train and apply, and being suitable for use with both GPU and CPU hardware setups. These reductions in timing and hardware requirements potentially allow the use of more powerful algorithms in HEP analyses, where models must be retrained frequently, sometimes at short notice, by small groups of researchers with limited hardware resources. Additionally, a new wrapper library for PyTorch called LUMINis presented, which incorporates all of the techniques studied.

Attribution methods provide insights into the decision-making of machine learning models like artificial neural networks. For a given input sample, they assign a relevance score to each individual input variable, such as the pixels of an image. In this work we adapt the information bottleneck concept for attribution. By adding noise to intermediate feature maps we restrict the flow of information and can quantify (in bits) how much information image regions provide. We compare our method against ten baselines using three different metrics on VGG-16 and ResNet-50, and find that our methods outperform all baselines in five out of six settings. The method's information-theoretic foundation provides an absolute frame of reference for attribution values (bits) and a guarantee that regions scored close to zero are not necessary for the network's decision. For reviews: https://openreview.net/forum?id=S1xWh1rYwB For code: https://github.com/BioroboticsLab/IBA

We focus on estimating emph{a priori} generalization error of two-layer ReLU neural networks (NNs) trained by mean squared error, which only depends on initial parameters and the target function, through the following research line. We first estimate emph{a priori} generalization error of finite-width two-layer ReLU NN with constraint of minimal norm solution, which is proved by cite{zhang2019type} to be an equivalent solution of a linearized (w.r.t. parameter) finite-width two-layer NN. As the width goes to infinity, the linearized NN converges to the NN in Neural Tangent Kernel (NTK) regime citep{jacot2018neural}. Thus, we can derive the emph{a priori} generalization error of two-layer ReLU NN in NTK regime. The distance between NN in a NTK regime and a finite-width NN with gradient training is estimated by cite{arora2019exact}. Based on the results in cite{arora2019exact}, our work proves an emph{a priori} generalization error bound of two-layer ReLU NNs. This estimate uses the intrinsic implicit bias of the minimum norm solution without requiring extra regularity in the loss function. This emph{a priori} estimate also implies that NN does not suffer from curse of dimensionality, and a small generalization error can be achieved without requiring exponentially large number of neurons. In addition the research line proposed in this paper can also be used to study other properties of the finite-width network, such as the posterior generalization error.

We focus on the challenge of finding a diverse collection of quality solutions on complex continuous domains. While quality diver-sity (QD) algorithms like Novelty Search with Local Competition (NSLC) and MAP-Elites are designed to generate a diverse range of solutions, these algorithms require a large number of evaluations for exploration of continuous spaces. Meanwhile, variants of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) are among the best-performing derivative-free optimizers in single-objective continuous domains. This paper proposes a new QD algorithm called Covariance Matrix Adaptation MAP-Elites (CMA-ME). Our new algorithm combines the self-adaptation techniques of CMA-ES with archiving and mapping techniques for maintaining diversity in QD. Results from experiments based on standard continuous optimization benchmarks show that CMA-ME finds better-quality solutions than MAP-Elites; similarly, results on the strategic game Hearthstone show that CMA-ME finds both a higher overall quality and broader diversity of strategies than both CMA-ES and MAP-Elites. Overall, CMA-ME more than doubles the performance of MAP-Elites using standard QD performance metrics. These results suggest that QD algorithms augmented by operators from state-of-the-art optimization algorithms can yield high-performing methods for simultaneously exploring and optimizing continuous search spaces, with significant applications to design, testing, and reinforcement learning among other domains.

This paper develops a general framework for analyzing asymptotics of $V$-statistics. Previous literature on limiting distribution mainly focuses on the cases when $n o infty$ with fixed kernel size $k$. Under some regularity conditions, we demonstrate asymptotic normality when $k$ grows with $n$ by utilizing existing results for $U$-statistics. The key in our approach lies in a mathematical reduction to $U$-statistics by designing an equivalent kernel for $V$-statistics. We also provide a unified treatment on variance estimation for both $U$- and $V$-statistics by observing connections to existing methods and proposing an empirically more accurate estimator. Ensemble methods such as random forests, where multiple base learners are trained and aggregated for prediction purposes, serve as a running example throughout the paper because they are a natural and flexible application of $V$-statistics.

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph $F$ into a large network $mathcal{G}$. We propose two complementary MCMC algorithms for sampling a random graph homomorphisms and establish bounds on their mixing times and concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neigborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also apply our framework for network clustering and classification problems using the Facebook100 dataset and Word Adjacency Networks of a set of classic novels.

Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often have an interesting theoretical interpretation in real problems. However, standard factor analysis is only applicable when the variables are scaled, which is often inappropriate, for example, in data obtained from questionnaires in the field of psychology,where the variables are often categorical. In this framework, we propose a factor model for the analysis of multivariate ordered and non-ordered polychotomous data. The inference procedure is done under the Bayesian approach via Markov chain Monte Carlo methods. Two Monte-Carlo simulation studies are presented to investigate the performance of this approach in terms of estimation bias, precision and assessment of the number of factors. We also illustrate the proposed method to analyze participants' responses to the Motivational State Questionnaire dataset, developed to study emotions in laboratory and field settings.

A deep neural network has relieved the burden of feature engineering by human experts, but comparable efforts are instead required to determine an effective architecture. On the other hands, as the size of a network has over-grown, a lot of resources are also invested to reduce its size. These problems can be addressed by sparsification of an over-complete model, which removes redundant parameters or connections by pruning them away after training or encouraging them to become zero during training. In general, however, these approaches are not fully differentiable and interrupt an end-to-end training process with the stochastic gradient descent in that they require either a parameter selection or a soft-thresholding step. In this paper, we propose a fully differentiable sparsification method for deep neural networks, which allows parameters to be exactly zero during training, and thus can learn the sparsified structure and the weights of networks simultaneously using the stochastic gradient descent. We apply the proposed method to various popular models in order to show its effectiveness.

A major difficulty of solving continuous POMDPs is to infer the multi-modal distribution of the unobserved true states and to make the planning algorithm dependent on the perceived uncertainty. We cast POMDP filtering and planning problems as two closely related Sequential Monte Carlo (SMC) processes, one over the real states and the other over the future optimal trajectories, and combine the merits of these two parts in a new model named the DualSMC network. In particular, we first introduce an adversarial particle filter that leverages the adversarial relationship between its internal components. Based on the filtering results, we then propose a planning algorithm that extends the previous SMC planning approach [Piche et al., 2018] to continuous POMDPs with an uncertainty-dependent policy. Crucially, not only can DualSMC handle complex observations such as image input but also it remains highly interpretable. It is shown to be effective in three continuous POMDP domains: the floor positioning domain, the 3D light-dark navigation domain, and a modified Reacher domain.

Boosting is one of the most successful ideas in machine learning. The most well-accepted explanations for the low generalization error of boosting algorithms such as AdaBoost stem from margin theory. The study of margins in the context of boosting algorithms was initiated by Schapire, Freund, Bartlett and Lee (1998) and has inspired numerous boosting algorithms and generalization bounds. To date, the strongest known generalization (upper bound) is the $k$th margin bound of Gao and Zhou (2013). Despite the numerous generalization upper bounds that have been proved over the last two decades, nothing is known about the tightness of these bounds. In this paper, we give the first margin-based lower bounds on the generalization error of boosted classifiers. Our lower bounds nearly match the $k$th margin bound and thus almost settle the generalization performance of boosted classifiers in terms of margins.

We study the problem of parameter estimation for a non-ergodic Gaussian Vasicek-type model defined as $dX_t=(mu+ heta X_t)dt+dG_t, tgeq0$ with unknown parameters $ heta>0$ and $muinR$, where $G$ is a Gaussian process. We provide least square-type estimators $widetilde{ heta}_T$ and $widetilde{mu}_T$ respectively for the drift parameters $ heta$ and $mu$ based on continuous-time observations ${X_t, tin[0,T]}$ as $T ightarrowinfty$.

Our aim is to derive some sufficient conditions on the driving Gaussian process $G$ in order to ensure that $widetilde{ heta}_T$ and $widetilde{mu}_T$ are strongly consistent, the limit distribution of $widetilde{ heta}_T$ is a Cauchy-type distribution and $widetilde{mu}_T$ is asymptotically normal. We apply our result to fractional Vasicek, subfractional Vasicek and bifractional Vasicek processes. In addition, this work extends the result of cite{EEO} studied in the case where $mu=0$.

We study the interplay of two important issues on Bayesian model selection (BMS): censoring and model misspecification. We consider additive accelerated failure time (AAFT), Cox proportional hazards and probit models, and a more general concave log-likelihood structure. A fundamental question is what solution can one hope BMS to provide, when (inevitably) models are misspecified. We show that asymptotically BMS keeps any covariate with predictive power for either the outcome or censoring times, and discards other covariates. Misspecification refers to assuming the wrong model or functional effect on the response, including using a finite basis for a truly non-parametric effect, or omitting truly relevant covariates. We argue for using simple models that are computationally practical yet attain good power to detect potentially complex effects, despite misspecification. Misspecification and censoring both have an asymptotically negligible effect on (suitably-defined) false positives, but their impact on power is exponential. We portray these issues via simple descriptions of early/late censoring and the drop in predictive accuracy due to misspecification. From a methods point of view, we consider local priors and a novel structure that combines local and non-local priors to enforce sparsity. We develop algorithms to capitalize on the AAFT tractability, approximations to AAFT and probit likelihoods giving significant computational gains, a simple augmented Gibbs sampler to hierarchically explore linear and non-linear effects, and an implementation in the R package mombf. We illustrate the proposed methods and others based on likelihood penalties via extensive simulations under misspecification and censoring. We present two applications concerning the effect of gene expression on colon and breast cancer.

Adaptive importance samplers are adaptive Monte Carlo algorithms to estimate expectations with respect to some target distribution which extit{adapt} themselves to obtain better estimators over a sequence of iterations. Although it is straightforward to show that they have the same $mathcal{O}(1/sqrt{N})$ convergence rate as standard importance samplers, where $N$ is the number of Monte Carlo samples, the behaviour of adaptive importance samplers over the number of iterations has been left relatively unexplored. In this work, we investigate an adaptation strategy based on convex optimisation which leads to a class of adaptive importance samplers termed extit{optimised adaptive importance samplers} (OAIS). These samplers rely on the iterative minimisation of the $chi^2$-divergence between an exponential-family proposal and the target. The analysed algorithms are closely related to the class of adaptive importance samplers which minimise the variance of the weight function. We first prove non-asymptotic error bounds for the mean squared errors (MSEs) of these algorithms, which explicitly depend on the number of iterations and the number of samples together. The non-asymptotic bounds derived in this paper imply that when the target belongs to the exponential family, the $L_2$ errors of the optimised samplers converge to the optimal rate of $mathcal{O}(1/sqrt{N})$ and the rate of convergence in the number of iterations are explicitly provided. When the target does not belong to the exponential family, the rate of convergence is the same but the asymptotic $L_2$ error increases by a factor $sqrt{ ho^star} > 1$, where $ ho^star - 1$ is the minimum $chi^2$-divergence between the target and an exponential-family proposal.

The Rosenbrock function is an ubiquitous benchmark problem for numerical optimisation, and variants have been proposed to test the performance of Markov Chain Monte Carlo algorithms. In this work we discuss the two-dimensional Rosenbrock density, its current $n$-dimensional extensions, and their advantages and limitations. We then propose a new extension to arbitrary dimensions called the Hybrid Rosenbrock distribution, which is composed of conditional normal kernels arranged in such a way that preserves the key features of the original kernel. Moreover, due to its structure, the Hybrid Rosenbrock distribution is analytically tractable and possesses several desirable properties, which make it an excellent test model for computational algorithms.

Deep networks run with low precision operations at inference time offer power and space advantages over high precision alternatives, but need to overcome the challenge of maintaining high accuracy as precision decreases. Here, we present a method for training such networks, Learned Step Size Quantization, that achieves the highest accuracy to date on the ImageNet dataset when using models, from a variety of architectures, with weights and activations quantized to 2-, 3- or 4-bits of precision, and that can train 3-bit models that reach full precision baseline accuracy. Our approach builds upon existing methods for learning weights in quantized networks by improving how the quantizer itself is configured. Specifically, we introduce a novel means to estimate and scale the task loss gradient at each weight and activation layer's quantizer step size, such that it can be learned in conjunction with other network parameters. This approach works using different levels of precision as needed for a given system and requires only a simple modification of existing training code.

In classification models fairness can be ensured by solving a constrained optimization problem. We focus on fairness constraints like Disparate Impact, Demographic Parity, and Equalized Odds, which are non-decomposable and non-convex. Researchers define convex surrogates of the constraints and then apply convex optimization frameworks to obtain fair classifiers. Surrogates serve only as an upper bound to the actual constraints, and convexifying fairness constraints might be challenging.

We propose a neural network-based framework, emph{FNNC}, to achieve fairness while maintaining high accuracy in classification. The above fairness constraints are included in the loss using Lagrangian multipliers. We prove bounds on generalization errors for the constrained losses which asymptotically go to zero. The network is optimized using two-step mini-batch stochastic gradient descent. Our experiments show that FNNC performs as good as the state of the art, if not better. The experimental evidence supplements our theoretical guarantees. In summary, we have an automated solution to achieve fairness in classification, which is easily extendable to many fairness constraints.

We propose a novel estimation procedure for scale-by-scale lead-lag relationships of financial assets observed at high-frequency in a non-synchronous manner. The proposed estimation procedure does not require any interpolation processing of original datasets and is applicable to those with highest time resolution available. Consistency of the proposed estimators is shown under the continuous-time framework that has been developed in our previous work Hayashi and Koike (2018). An empirical application to a quote dataset of the NASDAQ-100 assets identifies two types of lead-lag relationships at different time scales.

When the response mechanism is believed to be not missing at random (NMAR), a valid analysis requires stronger assumptions on the response mechanism than standard statistical methods would otherwise require. Semiparametric estimators have been developed under the model assumptions on the response mechanism. In this paper, a new statistical test is proposed to guarantee model identifiability without using any instrumental variable. Furthermore, we develop optimal semiparametric estimation for parameters such as the population mean. Specifically, we propose two semiparametric optimal estimators that do not require any model assumptions other than the response mechanism. Asymptotic properties of the proposed estimators are discussed. An extensive simulation study is presented to compare with some existing methods. We present an application of our method using Korean Labor and Income Panel Survey data.

Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of nonzero loadings in these combinations. In this paper we consider 8 different optimization formulations for computing a single sparse loading vector; these are obtained by combining the following factors: we employ two norms for measuring variance (L2, L1) and two sparsity-inducing norms (L0, L1), which are used in two different ways (constraint, penalty). Three of our formulations, notably the one with L0 constraint and L1 variance, have not been considered in the literature. We give a unifying reformulation which we propose to solve via a natural alternating maximization (AM) method. We show the the AM method is nontrivially equivalent to GPower (Journ'{e}e et al; JMLR 11:517--553, 2010) for all our formulations. Besides this, we provide 24 efficient parallel SPCA implementations: 3 codes (multi-core, GPU and cluster) for each of the 8 problems. Parallelism in the methods is aimed at i) speeding up computations (our GPU code can be 100 times faster than an efficient serial code written in C++), ii) obtaining solutions explaining more variance and iii) dealing with big data problems (our cluster code is able to solve a 357 GB problem in about a minute).

Heat waves resulting from prolonged extreme temperatures pose a significant risk to human health globally. Given the limitations of observations of extreme temperature, climate models are often used to characterize extreme temperature globally, from which one can derive quantities like return values to summarize the magnitude of a low probability event for an arbitrary geographic location. However, while these derived quantities are useful on their own, it is also often important to apply a spatial statistical model to such data in order to, e.g., understand how the spatial dependence properties of the return values vary over space and emulate the climate model for generating additional spatial fields with corresponding statistical properties. For these objectives, when modeling global data it is critical to use a nonstationary covariance function. Furthermore, given that the output of modern global climate models can be on the order of $mathcal{O}(10^4)$, it is important to utilize approximate Gaussian process methods to enable inference. In this paper, we demonstrate the application of methodology introduced in Risser and Turek (2020) to conduct a nonstationary and fully Bayesian analysis of a large data set of 20-year return values derived from an ensemble of global climate model runs with over 50,000 spatial locations. This analysis uses the freely available BayesNSGP software package for R.

The paper focuses on a novel approach for false-positive reduction (FPR) of nodule candidates in Computer-aided detection (CADe) system after suspicious lesions proposing stage. Unlike common decisions in medical image analysis, the proposed approach considers input data not as 2d or 3d image, but as a point cloud and uses deep learning models for point clouds. We found out that models for point clouds require less memory and are faster on both training and inference than traditional CNN 3D, achieves better performance and does not impose restrictions on the size of the input image, thereby the size of the nodule candidate. We propose an algorithm for transforming 3d CT scan data to point cloud. In some cases, the volume of the nodule candidate can be much smaller than the surrounding context, for example, in the case of subpleural localization of the nodule. Therefore, we developed an algorithm for sampling points from a point cloud constructed from a 3D image of the candidate region. The algorithm guarantees to capture both context and candidate information as part of the point cloud of the nodule candidate. An experiment with creating a dataset from an open LIDC-IDRI database for a feature of the FPR task was accurately designed, set up and described in detail. The data augmentation technique was applied to avoid overfitting and as an upsampling method. Experiments are conducted with PointNet, PointNet++ and DGCNN. We show that the proposed approach outperforms baseline CNN 3D models and demonstrates 85.98 FROC versus 77.26 FROC for baseline models.

We analyze risk factors correlated with the initial transmission growth rate of the COVID-19 pandemic. The number of cases follows an early exponential expansion; we chose as a starting point in each country the first day with 30 cases and used 12 days. We looked for linear correlations of the exponents with other variables, using 126 countries. We find a positive correlation with high C.L. with the following variables, with respective $p$-value: low Temperature ($4cdot10^{-7}$), high ratio of old vs.~working-age people ($3cdot10^{-6}$), life expectancy ($8cdot10^{-6}$), number of international tourists ($1cdot10^{-5}$), earlier epidemic starting date ($2cdot10^{-5}$), high level of contact in greeting habits ($6 cdot 10^{-5}$), lung cancer ($6 cdot 10^{-5}$), obesity in males ($1 cdot 10^{-4}$), urbanization ($2cdot10^{-4}$), cancer prevalence ($3 cdot 10^{-4}$), alcohol consumption ($0.0019$), daily smoking prevalence ($0.0036$), UV index ($0.004$, smaller sample, 73 countries), low Vitamin D levels ($p$-value $0.002-0.006$, smaller sample, $sim 50$ countries). There is highly significant correlation also with blood type: positive correlation with RH- ($2cdot10^{-5}$) and A+ ($2cdot10^{-3}$), negative correlation with B+ ($2cdot10^{-4}$). We also find positive correlation with moderate C.L. ($p$-value of $0.02sim0.03$) with: CO$_2$ emissions, type-1 diabetes, low vaccination coverage for Tuberculosis (BCG). Several such variables are correlated with each other and so they likely have common interpretations. We also analyzed the possible existence of a bias: countries with low GDP-per capita, typically located in warm regions, might have less intense testing and we discuss correlation with the above variables.

In this paper we introduce plan2vec, an unsupervised representation learning approach that is inspired by reinforcement learning. Plan2vec constructs a weighted graph on an image dataset using near-neighbor distances, and then extrapolates this local metric to a global embedding by distilling path-integral over planned path. When applied to control, plan2vec offers a way to learn goal-conditioned value estimates that are accurate over long horizons that is both compute and sample efficient. We demonstrate the effectiveness of plan2vec on one simulated and two challenging real-world image datasets. Experimental results show that plan2vec successfully amortizes the planning cost, enabling reactive planning that is linear in memory and computation complexity rather than exhaustive over the entire state space.

We present LCE, a Local Cascade Ensemble for traditional (tabular) multivariate data classification, and its extension LCEM for Multivariate Time Series (MTS) classification. LCE is a new hybrid ensemble method that combines an explicit boosting-bagging approach to handle the usual bias-variance tradeoff faced by machine learning models and an implicit divide-and-conquer approach to individualize classifier errors on different parts of the training data. Our evaluation firstly shows that the hybrid ensemble method LCE outperforms the state-of-the-art classifiers on the UCI datasets and that LCEM outperforms the state-of-the-art MTS classifiers on the UEA datasets. Furthermore, LCEM provides explainability by design and manifests robust performance when faced with challenges arising from continuous data collection (different MTS length, missing data and noise).

Increasing number of sectors which affect human lives, are using Machine Learning (ML) tools. Hence the need for understanding their working mechanism and evaluating their fairness in decision-making, are becoming paramount, ushering in the era of Explainable AI (XAI). In this contribution we introduced a few intrinsically interpretable models which are also capable of dealing with missing values, in addition to extracting knowledge from the dataset and about the problem. These models are also capable of visualisation of the classifier and decision boundaries: they are the angle based variants of Learning Vector Quantization. We have demonstrated the algorithms on a synthetic dataset and a real-world one (heart disease dataset from the UCI repository). The newly developed classifiers helped in investigating the complexities of the UCI dataset as a multiclass problem. The performance of the developed classifiers were comparable to those reported in literature for this dataset, with additional value of interpretability, when the dataset was treated as a binary class problem.

The $p$-tensor Curie-Weiss model is a two-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic has a linear term and a term with degree $p geq 2$. This is a special case of the tensor Ising model and the natural generalization of the matrix Curie-Weiss model, which provides a convenient mathematical abstraction for capturing, not just pairwise, but higher-order dependencies. In this paper we provide a complete description of the limiting properties of the maximum likelihood (ML) estimates of the natural parameters, given a single sample from the $p$-tensor Curie-Weiss model, for $p geq 3$, complementing the well-known results in the matrix ($p=2$) case (Comets and Gidas (1991)). Our results unearth various new phase transitions and surprising limit theorems, such as the existence of a 'critical' curve in the parameter space, where the limiting distribution of the ML estimates is a mixture with both continuous and discrete components. The number of mixture components is either two or three, depending on, among other things, the sign of one of the parameters and the parity of $p$. Another interesting revelation is the existence of certain 'special' points in the parameter space where the ML estimates exhibit a superefficiency phenomenon, converging to a non-Gaussian limiting distribution at rate $N^{frac{3}{4}}$. We discuss how these results can be used to construct confidence intervals for the model parameters and, as a byproduct of our analysis, obtain limit theorems for the sample mean, which provide key insights into the statistical properties of the model.

In Canada, financial advisors and dealers by provincial securities commissions, and those self-regulatory organizations charged with direct regulation over investment dealers and mutual fund dealers, respectively to collect and maintain Know Your Client (KYC) information, such as their age or risk tolerance, for investor accounts. With this information, investors, under their advisor's guidance, make decisions on their investments which are presumed to be beneficial to their investment goals. Our unique dataset is provided by a financial investment dealer with over 50,000 accounts for over 23,000 clients. We use a modified behavioural finance recency, frequency, monetary model for engineering features that quantify investor behaviours, and machine learning clustering algorithms to find groups of investors that behave similarly. We show that the KYC information collected does not explain client behaviours, whereas trade and transaction frequency and volume are most informative. We believe the results shown herein encourage financial regulators and advisors to use more advanced metrics to better understand and predict investor behaviours.

This paper considers the problem of estimation of the Fisher information for location from a random sample of size $n$. First, an estimator proposed by Bhattacharya is revisited and improved convergence rates are derived. Second, a new estimator, termed a clipped estimator, is proposed. Superior upper bounds on the rates of convergence can be shown for the new estimator compared to the Bhattacharya estimator, albeit with different regularity conditions. Third, both of the estimators are evaluated for the practically relevant case of a random variable contaminated by Gaussian noise. Moreover, using Brown's identity, which relates the Fisher information and the minimum mean squared error (MMSE) in Gaussian noise, two corresponding consistent estimators for the MMSE are proposed. Simulation examples for the Bhattacharya estimator and the clipped estimator as well as the MMSE estimators are presented. The examples demonstrate that the clipped estimator can significantly reduce the required sample size to guarantee a specific confidence interval compared to the Bhattacharya estimator.

Disaggregation regression has become an important tool in spatial disease mapping for making fine-scale predictions of disease risk from aggregated response data. By including high resolution covariate information and modelling the data generating process on a fine scale, it is hoped that these models can accurately learn the relationships between covariates and response at a fine spatial scale. However, validating these high resolution predictions can be a challenge, as often there is no data observed at this spatial scale. In this study, disaggregation regression was performed on simulated data in various settings and the resulting fine-scale predictions are compared to the simulated ground truth. Performance was investigated with varying numbers of data points, sizes of aggregated areas and levels of model misspecification. The effectiveness of cross validation on the aggregate level as a measure of fine-scale predictive performance was also investigated. Predictive performance improved as the number of observations increased and as the size of the aggregated areas decreased. When the model was well-specified, fine-scale predictions were accurate even with small numbers of observations and large aggregated areas. Under model misspecification predictive performance was significantly worse for large aggregated areas but remained high when response data was aggregated over smaller regions. Cross-validation correlation on the aggregate level was a moderately good predictor of fine-scale predictive performance. While the simulations are unlikely to capture the nuances of real-life response data, this study gives insight into the effectiveness of disaggregation regression in different contexts.

We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the learning process by adding the residuals of a system of Partial Differential Equations to the loss function. Our PINN is supervised with realistic ultrasonic surface acoustic wave data acquired at a frequency of 5 MHz. The ultrasonic surface wave data is represented as a surface deformation on the top surface of a metal plate, measured by using the method of laser vibrometry. The PINN is physically informed by the acoustic wave equation and its convergence is sped up using adaptive activation functions. The adaptive activation function uses a scalable hyperparameter in the activation function, which is optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The usage of adaptive activation function significantly improves the convergence, notably observed in the current study. We use PINNs to estimate the speed of sound of the metal plate, which we do with an error of 1\%, and then, by allowing the speed of sound to be space dependent, we identify and characterize the crack as the positions where the speed of sound has decreased. Our study also shows the effect of sub-sampling of the data on the sensitivity of sound speed estimates. More broadly, the resulting model shows a promising deep neural network model for ill-posed inverse problems.

In many Machine Learning domains, datasets are characterized by highly imbalanced and overlapping classes. Particularly in the medical domain, a specific list of symptoms can be labeled as one of various different conditions. Some of these conditions may be more prevalent than others by several orders of magnitude. Here we present a novel unsupervised Domain Adaptation scheme for such datasets. The scheme, based on a specific type of Quantification, is designed to work under both label and conditional shifts. It is demonstrated on datasets generated from Electronic Health Records and provides high quality results for both Quantification and Domain Adaptation in very challenging scenarios. Potential benefits of using this scheme in the current COVID-19 outbreak, for estimation of prevalence and probability of infection, are discussed.

Early detection of patients vulnerable to infections acquired in the hospital environment is a challenge in current health systems given the impact that such infections have on patient mortality and healthcare costs. This work is focused on both the identification of risk factors and the prediction of healthcare-associated infections in intensive-care units by means of machine-learning methods. The aim is to support decision making addressed at reducing the incidence rate of infections. In this field, it is necessary to deal with the problem of building reliable classifiers from imbalanced datasets. We propose a clustering-based undersampling strategy to be used in combination with ensemble classifiers. A comparative study with data from 4616 patients was conducted in order to validate our proposal. We applied several single and ensemble classifiers both to the original dataset and to data preprocessed by means of different resampling methods. The results were analyzed by means of classic and recent metrics specifically designed for imbalanced data classification. They revealed that the proposal is more efficient in comparison with other approaches.

This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information they decide to wait for service or to leave the system. The main objective is to estimate the customers' patience-level distribution and the corresponding potential arrival rate, using knowledge of the actual workload process only. We cast the system as a queueing model, so as to evaluate the corresponding likelihood function. Estimating the unknown parameters relying on a maximum likelihood procedure, we prove strong consistency and derive the asymptotic distribution of the estimation error. Several applications and extensions of the method are discussed. In particular, we indicate how our method generalizes to a multi-server setting. The performance of our approach is assessed through a series of numerical experiments. By fitting parameters of hyperexponential and generalized-hyperexponential distributions our method provides a robust estimation framework for any continuous patience-level distribution.

Simplicity is the ultimate sophistication. Differentiable Architecture Search (DARTS) has now become one of the mainstream paradigms of neural architecture search. However, it largely suffers from several disturbing factors of optimization process whose results are unstable to reproduce. FairDARTS points out that skip connections natively have an unfair advantage in exclusive competition which primarily leads to dramatic performance collapse. While FairDARTS turns the unfair competition into a collaborative one, we instead impede such unfair advantage by injecting unbiased random noise into skip operations' output. In effect, the optimizer should perceive this difficulty at each training step and refrain from overshooting on skip connections, but in a long run it still converges to the right solution area since no bias is added to the gradient. We name this novel approach as NoisyDARTS. Our experiments on CIFAR-10 and ImageNet attest that it can effectively break the skip connection's unfair advantage and yield better performance. It generates a series of models that achieve state-of-the-art results on both datasets.

As an important type of reinforcement learning algorithms, actor-critic (AC) and natural actor-critic (NAC) algorithms are often executed in two ways for finding optimal policies. In the first nested-loop design, actor's one update of policy is followed by an entire loop of critic's updates of the value function, and the finite-sample analysis of such AC and NAC algorithms have been recently well established. The second two time-scale design, in which actor and critic update simultaneously but with different learning rates, has much fewer tuning parameters than the nested-loop design and is hence substantially easier to implement. Although two time-scale AC and NAC have been shown to converge in the literature, the finite-sample convergence rate has not been established. In this paper, we provide the first such non-asymptotic convergence rate for two time-scale AC and NAC under Markovian sampling and with actor having general policy class approximation. We show that two time-scale AC requires the overall sample complexity at the order of $mathcal{O}(epsilon^{-2.5}log^3(epsilon^{-1}))$ to attain an $epsilon$-accurate stationary point, and two time-scale NAC requires the overall sample complexity at the order of $mathcal{O}(epsilon^{-4}log^2(epsilon^{-1}))$ to attain an $epsilon$-accurate global optimal point. We develop novel techniques for bounding the bias error of the actor due to dynamically changing Markovian sampling and for analyzing the convergence rate of the linear critic with dynamically changing base functions and transition kernel.

In the field of numerical weather prediction (NWP), the probabilistic distribution of the future state of the atmosphere is sampled with Monte-Carlo-like simulations, called ensembles. These ensembles have deficiencies (such as conditional biases) that can be corrected thanks to statistical post-processing methods. Several ensembles exist and may be corrected with different statistiscal methods. A further step is to combine these raw or post-processed ensembles. The theory of prediction with expert advice allows us to build combination algorithms with theoretical guarantees on the forecast performance. This article adapts this theory to the case of probabilistic forecasts issued as step-wise cumulative distribution functions (CDF). The theory is applied to wind speed forecasting, by combining several raw or post-processed ensembles, considered as CDFs. The second goal of this study is to explore the use of two forecast performance criteria: the Continous ranked probability score (CRPS) and the Jolliffe-Primo test. Comparing the results obtained with both criteria leads to reconsidering the usual way to build skillful probabilistic forecasts, based on the minimization of the CRPS. Minimizing the CRPS does not necessarily produce reliable forecasts according to the Jolliffe-Primo test. The Jolliffe-Primo test generally selects reliable forecasts, but could lead to issuing suboptimal forecasts in terms of CRPS. It is proposed to use both criterion to achieve reliable and skillful probabilistic forecasts.