Zhengwei Liu, Qi Li, Fukang Zhu.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 251--272.

Abstract:
To predict time series of counts with small values and remarkable fluctuations, an available model is the $r$ states random environment process based on the negative binomial thinning operator and the geometric marginal. However, we argue that the aforementioned model may suffer from the following two drawbacks. First, under the condition of no prior information, the overdispersed property of the geometric distribution may cause the predictions fluctuate greatly. Second, because of the constraints on the model parameters, some estimated parameters are close to zero in real-data examples, which may not objectively reveal the correlation relationship. For the first drawback, an $r$ states random environment process based on the binomial thinning operator and the Poisson marginal is introduced. For the second drawback, we propose a generalized $r$ states random environment integer-valued autoregressive model based on the binomial thinning operator to model fluctuations of data. Yule–Walker and conditional maximum likelihood estimates are considered and their performances are assessed via simulation studies. Two real-data sets are conducted to illustrate the better performances of the proposed models compared with some existing models.

Fredy Castellares, Artur J. Lemonte, Marcos A. C. Santos.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 90--111.

Abstract:
We introduce a two-parameter discrete distribution that may have a zero vertex and can be useful for modeling overdispersion. The discrete Nielsen distribution generalizes the Fisher logarithmic (i.e., logarithmic series) and Stirling type I distributions in the sense that both can be considered displacements of the Nielsen distribution. We provide a comprehensive account of the structural properties of the new discrete distribution. We also show that the Nielsen distribution is infinitely divisible. We discuss maximum likelihood estimation of the model parameters and provide a simple method to find them numerically. The usefulness of the proposed distribution is illustrated by means of three real data sets to prove its versatility in practical applications.

Flávio B. Gonçalves, Marcos O. Prates, Victor Hugo Lachos.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 51--70.

Abstract:
In this paper, we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture corresponds to one possible model within the symmetrical class of normal independent distributions. Naturally, the Gaussian model is one of the possibilities. This allows for a simultaneous analysis based on the posterior probability of each model. Inference is performed via Markov chain Monte Carlo—a Gibbs sampler with Metropolis–Hastings steps for a class of parameters. Simulated examples highlight the advantages of this approach compared to a segregated analysis based on arbitrarily chosen model selection criteria. Examples with real data are presented and an extension to censored linear regression is introduced and discussed.

Sylvia Frühwirth-Schnatter.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 4, 706--733.

Abstract:
Finite mixture models and their extensions to Markov mixture and mixture of experts models are very popular in analysing data of various kind. A challenge for these models is choosing the number of components based on marginal likelihoods. The present paper suggests two innovative, generic bridge sampling estimators of the marginal likelihood that are based on constructing balanced importance densities from the conditional densities arising during Gibbs sampling. The full permutation bridge sampling estimator is derived from considering all possible permutations of the mixture labels for a subset of these densities. For the double random permutation bridge sampling estimator, two levels of random permutations are applied, first to permute the labels of the MCMC draws and second to randomly permute the labels of the conditional densities arising during Gibbs sampling. Various applications show very good performance of these estimators in comparison to importance and to reciprocal importance sampling estimators derived from the same importance densities.

Achillefs Tzioufas.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 3, 674--684.

Abstract:
The epidemic process on a graph is considered for which infectious contacts occur at rate which depends on whether a susceptible is infected for the first time or not. We show that the Vasershtein coupling extends if and only if secondary infections occur at rate which is greater than that of initial ones. Nonetheless we show that, with respect to the probability of occurrence of an infinite epidemic, the said proviso may be dropped regarding the totally asymmetric process in one dimension, thus settling in the affirmative this special case of the conjecture for arbitrary graphs due to [ Ann. Appl. Probab. 13 (2003) 669–690].

Kazuki Okamura.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 3, 586--637.

Abstract:
We consider a random object that is associated with both random walks and random media, specifically, the superposition of a configuration of subcritical Bernoulli percolation on an infinite connected graph and the trace of the simple random walk on the same graph. We investigate asymptotics for the number of vertices of the enlargement of the trace of the walk until a fixed time, when the time tends to infinity. This process is more highly self-interacting than the range of random walk, which yields difficulties. We show a law of large numbers on vertex-transitive transient graphs. We compare the process on a vertex-transitive graph with the process on a finitely modified graph of the original vertex-transitive graph and show their behaviors are similar. We show that the process fluctuates almost surely on a certain non-vertex-transitive graph. On the two-dimensional integer lattice, by investigating the size of the boundary of the trace, we give an estimate for variances of the process implying a law of large numbers. We give an example of a graph with unbounded degrees on which the process behaves in a singular manner. As by-products, some results for the range and the boundary, which will be of independent interest, are obtained.

Davide Gabrielli, Ida Germana Minelli.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 3, 558--585.

Abstract:
Stochastic monotonicity is a well-known partial order relation between probability measures defined on the same partially ordered set. Strassen theorem establishes equivalence between stochastic monotonicity and the existence of a coupling compatible with respect to the partial order. We consider the case of a countable set and introduce the class of finitely decomposable flows on a directed acyclic graph associated to the partial order. We show that a probability measure stochastically dominates another probability measure if and only if there exists a finitely decomposable flow having divergence given by the difference of the two measures. We illustrate the result with some examples.

Christian Rau.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 3, 549--557.

Abstract:
We revisit a shape inversion formula derived by Panaretos in the context of a particle density estimation problem with unknown rotation of the particle. A distribution is presented which imitates, or “fakes”, the uniformity or Haar distribution that is part of that formula.

Norbert Hirschauer, Sven Grüner, Oliver Mußhoff, Claudia Becker, Antje Jantsch.

Source: Statistics Surveys, Volume 14, 71--91.

Abstract:
Besides the inferential errors that abound in the interpretation of $p$-values, the probabilistic pre-conditions (i.e. random sampling or equivalent) for using them at all are not often met by observational studies in the social sciences. This paper systematizes different sampling designs and discusses the restrictive requirements of data collection that are the indispensable prerequisite for using $p$-values.

Umberto Amato, Anestis Antoniadis, Italia De Feis.

Source: Statistics Surveys, Volume 14, 32--70.

Abstract:
We present and compare some nonparametric estimation methods (wavelet and/or spline-based) designed to recover a one-dimensional piecewise-smooth regression function in both a fixed equidistant or not equidistant design regression model and a random design model. Wavelet methods are known to be very competitive in terms of denoising and compression, due to the simultaneous localization property of a function in time and frequency. However, boundary assumptions, such as periodicity or symmetry, generate bias and artificial wiggles which degrade overall accuracy. Simple methods have been proposed in the literature for reducing the bias at the boundaries. We introduce new ones based on adaptive combinations of two estimators. The underlying idea is to combine a highly accurate method for non-regular functions, e.g., wavelets, with one well behaved at boundaries, e.g., Splines or Local Polynomial. We provide some asymptotic optimal results supporting our approach. All the methods can handle data with a random design. We also sketch some generalization to the multidimensional setting. To study the performance of the proposed approaches we have conducted an extensive set of simulations on synthetic data. An interesting regression analysis of two real data applications using these procedures unambiguously demonstrates their effectiveness.

Si Cheng, Daniel J. Eck, Forrest W. Crawford.

Source: Statistics Surveys, Volume 14, 1--31.

Abstract:
A finite set is “hidden” if its elements are not directly enumerable or if its size cannot be ascertained via a deterministic query. In public health, epidemiology, demography, ecology and intelligence analysis, researchers have developed a wide variety of indirect statistical approaches, under different models for sampling and observation, for estimating the size of a hidden set. Some methods make use of random sampling with known or estimable sampling probabilities, and others make structural assumptions about relationships (e.g. ordering or network information) between the elements that comprise the hidden set. In this review, we describe models and methods for learning about the size of a hidden finite set, with special attention to asymptotic properties of estimators. We study the properties of these methods under two asymptotic regimes, “infill” in which the number of fixed-size samples increases, but the population size remains constant, and “outfill” in which the sample size and population size grow together. Statistical properties under these two regimes can be dramatically different.

Pierre Lafaye de Micheaux, Benoît Liquet, Matthew Sutton.

Source: Statistics Surveys, Volume 13, 119--149.

Abstract:
Partial Least Squares (PLS) methods have been heavily exploited to analyse the association between two blocks of data. These powerful approaches can be applied to data sets where the number of variables is greater than the number of observations and in the presence of high collinearity between variables. Different sparse versions of PLS have been developed to integrate multiple data sets while simultaneously selecting the contributing variables. Sparse modeling is a key factor in obtaining better estimators and identifying associations between multiple data sets. The cornerstone of the sparse PLS methods is the link between the singular value decomposition (SVD) of a matrix (constructed from deflated versions of the original data) and least squares minimization in linear regression. We review four popular PLS methods for two blocks of data. A unified algorithm is proposed to perform all four types of PLS including their regularised versions. We present various approaches to decrease the computation time and show how the whole procedure can be scalable to big data sets. The bigsgPLS R package implements our unified algorithm and is available at https://github.com/matt-sutton/bigsgPLS .

Norbert Hirschauer, Sven Grüner, Oliver Mußhoff, Claudia Becker.

Source: Statistics Surveys, Volume 12, 136--172.

Abstract:
Data on how many scientific findings are reproducible are generally bleak and a wealth of papers have warned against misuses of the $p$-value and resulting false findings in recent years. This paper discusses the question of what we can(not) learn from the $p$-value, which is still widely considered as the gold standard of statistical validity. We aim to provide a non-technical and easily accessible resource for statistical practitioners who wish to spot and avoid misinterpretations and misuses of statistical significance tests. For this purpose, we first classify and describe the most widely discussed (“classical”) pitfalls of significance testing, and review published work on these misuses with a focus on regression-based “confirmatory” study. This includes a description of the single-study bias and a simulation-based illustration of how proper meta-analysis compares to misleading significance counts (“vote counting”). Going beyond the classical pitfalls, we also use simulation to provide intuition that relying on the statistical estimate “$p$-value” as a measure of evidence without considering its sample-to-sample variability falls short of the mark even within an otherwise appropriate interpretation. We conclude with a discussion of the exigencies of informed approaches to statistical inference and corresponding institutional reforms.

Zeinab Mashreghi, David Haziza, Christian Léger.

Source: Statistics Surveys, Volume 10, 1--52.

Abstract:
We review bootstrap methods in the context of survey data where the effect of the sampling design on the variability of estimators has to be taken into account. We present the methods in a unified way by classifying them in three classes: pseudo-population, direct, and survey weights methods. We cover variance estimation and the construction of confidence intervals for stratified simple random sampling as well as some unequal probability sampling designs. We also address the problem of variance estimation in presence of imputation to compensate for item non-response.

Clément Marteau, Theofanis Sapatinas.

Source: Statistics Surveys, Volume 9, 253--297.

Abstract:
We are concerned with minimax signal detection. In this setting, we discuss non-asymptotic and asymptotic approaches through a unified treatment. In particular, we consider a Gaussian sequence model that contains classical models as special cases, such as, direct, well-posed inverse and ill-posed inverse problems. Working with certain ellipsoids in the space of squared-summable sequences of real numbers, with a ball of positive radius removed, we compare the construction of lower and upper bounds for the minimax separation radius (non-asymptotic approach) and the minimax separation rate (asymptotic approach) that have been proposed in the literature. Some additional contributions, bringing to light links between non-asymptotic and asymptotic approaches to minimax signal, are also presented. An example of a mildly ill-posed inverse problem is used for illustrative purposes. In particular, it is shown that tools used to derive ‘asymptotic’ results can be exploited to draw ‘non-asymptotic’ conclusions, and vice-versa. In order to enhance our understanding of these two minimax signal detection paradigms, we bring into light hitherto unknown similarities and links between non-asymptotic and asymptotic approaches.

Didier Chauveau, David R. Hunter, Michael Levine.

Source: Statistics Surveys, Volume 9, 1--31.

Abstract:
The conditional independence assumption for nonparametric multivariate finite mixture models, a weaker form of the well-known conditional independence assumption for random effects models for longitudinal data, is the subject of an increasing number of theoretical and algorithmic developments in the statistical literature. After presenting a survey of this literature, including an in-depth discussion of the all-important identifiability results, this article describes and extends an algorithm for estimation of the parameters in these models. The algorithm works for any number of components in three or more dimensions. It possesses a descent property and can be easily adapted to situations where the data are grouped in blocks of conditionally independent variables. We discuss how to adapt this algorithm to various location-scale models that link component densities, and we even adapt it to a particular class of univariate mixture problems in which the components are assumed symmetric. We give a bandwidth selection procedure for our algorithm. Finally, we demonstrate the effectiveness of our algorithm using a simulation study and two psychometric datasets.

Oleksandr Sverdlov, Weng Kee Wong, Yevgen Ryeznik.

Source: Statistics Surveys, Volume 8, 2--44.

Abstract:
Adaptive clinical trials are becoming increasingly popular research designs for clinical investigation. Adaptive designs are particularly useful in phase I cancer studies where clinical data are scant and the goals are to assess the drug dose-toxicity profile and to determine the maximum tolerated dose while minimizing the number of study patients treated at suboptimal dose levels. In the current work we give an overview of adaptive design methods for phase I cancer trials. We find that modern statistical literature is replete with novel adaptive designs that have clearly defined objectives and established statistical properties, and are shown to outperform conventional dose finding methods such as the 3+3 design, both in terms of statistical efficiency and in terms of minimizing the number of patients treated at highly toxic or nonefficacious doses. We discuss statistical, logistical, and regulatory aspects of these designs and present some links to non-commercial statistical software for implementing these methods in practice.

Johan A.K. Suykens, Carlos Alzate, Kristiaan Pelckmans

Source: Statist. Surv., Volume 4, 148--183.

Abstract:
This paper discusses the role of primal and (Lagrange) dual model representations in problems of supervised and unsupervised learning. The specification of the estimation problem is conceived at the primal level as a constrained optimization problem. The constraints relate to the model which is expressed in terms of the feature map. From the conditions for optimality one jointly finds the optimal model representation and the model estimate. At the dual level the model is expressed in terms of a positive definite kernel function, which is characteristic for a support vector machine methodology. It is discussed how least squares support vector machines are playing a central role as core models across problems of regression, classification, principal component analysis, spectral clustering, canonical correlation analysis, dimensionality reduction and data visualization.

Sophie Achard, Jean-François Coeurjolly

Source: Statist. Surv., Volume 4, 117--147.

Abstract:
This paper gives an overview of the problem of estimating the Hurst parameter of a fractional Brownian motion when the data are observed with outliers and/or with an additive noise by using methods based on discrete variations. We show that the classical estimation procedure based on the log-linearity of the variogram of dilated series is made more robust to outliers and/or an additive noise by considering sample quantiles and trimmed means of the squared series or differences of empirical variances. These different procedures are compared and discussed through a large simulation study and are implemented in the R package dvfBm.

Volodymyr Melnykov, Ranjan Maitra

Source: Statist. Surv., Volume 4, 80--116.

Abstract:
Finite mixture models have a long history in statistics, having been used to model population heterogeneity, generalize distributional assumptions, and lately, for providing a convenient yet formal framework for clustering and classification. This paper provides a detailed review into mixture models and model-based clustering. Recent trends as well as open problems in the area are also discussed.

Arctic sea ice extent (SIE) in September 2019 ranked second-to-lowest in history and is trending downward. The understanding of how internal variability amplifies the effects of external $ ext{CO}_2$ forcing is still limited. We propose the VARCTIC, which is a Vector Autoregression (VAR) designed to capture and extrapolate Arctic feedback loops. VARs are dynamic simultaneous systems of equations, routinely estimated to predict and understand the interactions of multiple macroeconomic time series. Hence, the VARCTIC is a parsimonious compromise between fullblown climate models and purely statistical approaches that usually offer little explanation of the underlying mechanism. Our "business as usual" completely unconditional forecast has SIE hitting 0 in September by the 2060s. Impulse response functions reveal that anthropogenic $ ext{CO}_2$ emission shocks have a permanent effect on SIE - a property shared by no other shock. Further, we find Albedo- and Thickness-based feedbacks to be the main amplification channels through which $ ext{CO}_2$ anomalies impact SIE in the short/medium run. Conditional forecast analyses reveal that the future path of SIE crucially depends on the evolution of $ ext{CO}_2$ emissions, with outcomes ranging from recovering SIE to it reaching 0 in the 2050s. Finally, Albedo and Thickness feedbacks are shown to play an important role in accelerating the speed at which predicted SIE is heading towards 0.

Methods for generating synthetic data have become of increasing importance to build large datasets required for Convolution Neural Networks (CNN) based deep learning techniques for a wide range of computer vision applications. In this work, we extend existing methodologies to show how 2D thermal facial data can be mapped to provide 3D facial models. For the proposed research work we have used tufts datasets for generating 3D varying face poses by using a single frontal face pose. The system works by refining the existing image quality by performing fusion based image preprocessing operations. The refined outputs have better contrast adjustments, decreased noise level and higher exposedness of the dark regions. It makes the facial landmarks and temperature patterns on the human face more discernible and visible when compared to original raw data. Different image quality metrics are used to compare the refined version of images with original images. In the next phase of the proposed study, the refined version of images is used to create 3D facial geometry structures by using Convolution Neural Networks (CNN). The generated outputs are then imported in blender software to finally extract the 3D thermal facial outputs of both males and females. The same technique is also used on our thermal face data acquired using prototype thermal camera (developed under Heliaus EU project) in an indoor lab environment which is then used for generating synthetic 3D face data along with varying yaw face angles and lastly facial depth map is generated.

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.

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.

Supervised machine learning algorithms have seen spectacular advances and surpassed human level performance in a wide range of specific applications. However, using complex ensemble or deep learning algorithms typically results in black box models, where the path leading to individual predictions cannot be followed in detail. In order to address this issue, we propose the novel "Cyclic Boosting" machine learning algorithm, which allows to efficiently perform accurate regression and classification tasks while at the same time allowing a detailed understanding of how each individual prediction was made.

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.

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.

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.

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).

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.

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.

In this paper, we propose a new procedure to build a structural-factor model for a vector unit-root time series. For a $p$-dimensional unit-root process, we assume that each component consists of a set of common factors, which may be unit-root non-stationary, and a set of stationary components, which contain the cointegrations among the unit-root processes. To further reduce the dimensionality, we also postulate that the stationary part of the series is a nonsingular linear transformation of certain common factors and idiosyncratic white noise components as in Gao and Tsay (2019a, b). The estimation of linear loading spaces of the unit-root factors and the stationary components is achieved by an eigenanalysis of some nonnegative definite matrix, and the separation between the stationary factors and the white noises is based on an eigenanalysis and a projected principal component analysis. Asymptotic properties of the proposed method are established for both fixed $p$ and diverging $p$ as the sample size $n$ tends to infinity. Both simulated and real examples are used to demonstrate the performance of the proposed method in finite samples.

The ability of intelligent agents to learn and remember multiple tasks sequentially is crucial to achieving artificial general intelligence. Many continual learning (CL) methods have been proposed to overcome catastrophic forgetting. Catastrophic forgetting notoriously impedes the sequential learning of neural networks as the data of previous tasks are unavailable. In this paper we focus on class incremental learning, a challenging CL scenario, in which classes of each task are disjoint and task identity is unknown during test. For this scenario, generative replay is an effective strategy which generates and replays pseudo data for previous tasks to alleviate catastrophic forgetting. However, it is not trivial to learn a generative model continually for relatively complex data. Based on recently proposed orthogonal weight modification (OWM) algorithm which can keep previously learned input-output mappings invariant approximately when learning new tasks, we propose to directly generate and replay feature. Empirical results on image and text datasets show our method can improve OWM consistently by a significant margin while conventional generative replay always results in a negative effect. Our method also beats a state-of-the-art generative replay method and is competitive with a strong baseline based on real data storage.

Recent advancements in diagnostic learning and development of gesture-based human machine interfaces have driven surface electromyography (sEMG) towards significant importance. Analysis of hand gestures requires an accurate assessment of sEMG signals. The proposed work presents a novel sequential master-slave architecture consisting of deep neural networks (DNNs) for classification of signs from the Indian sign language using signals recorded from multiple sEMG channels. The performance of the master-slave network is augmented by leveraging additional synthetic feature data generated by long short term memory networks. Performance of the proposed network is compared to that of a conventional DNN prior to and after the addition of synthetic data. Up to 14% improvement is observed in the conventional DNN and up to 9% improvement in master-slave network on addition of synthetic data with an average accuracy value of 93.5% asserting the suitability of the proposed approach.

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. Recent advances in sparse identification show encouraging success in distilling closed-form governing equations from data for a wide range of nonlinear dynamical systems. However, the fundamental bottleneck of this approach lies in the robustness and scalability with respect to data scarcity and noise. This work introduces a novel physics-informed deep learning framework to discover governing partial differential equations (PDEs) from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this approach seamlessly integrates the strengths of deep neural networks for rich representation learning, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the PDEs. The efficacy and robustness of this method are demonstrated on discovering a variety of PDE systems with different levels of data scarcity and noise. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.

Hierarchical abstraction and curiosity-driven exploration are two common paradigms in current reinforcement learning approaches to break down difficult problems into a sequence of simpler ones and to overcome reward sparsity. However, there is a lack of approaches that combine these paradigms, and it is currently unknown whether curiosity also helps to perform the hierarchical abstraction. As a novelty and scientific contribution, we tackle this issue and develop a method that combines hierarchical reinforcement learning with curiosity. Herein, we extend a contemporary hierarchical actor-critic approach with a forward model to develop a hierarchical notion of curiosity. We demonstrate in several continuous-space environments that curiosity approximately doubles the learning performance and success rates for most of the investigated benchmarking problems.

Graph Neural Networks (GNNs) are powerful and flexible neural networks that use the naturally sparse connectivity information of the data. GNNs represent this connectivity as sparse matrices, which have lower arithmetic intensity and thus higher communication costs compared to dense matrices, making GNNs harder to scale to high concurrencies than convolutional or fully-connected neural networks.

We present a family of parallel algorithms for training GNNs. These algorithms are based on their counterparts in dense and sparse linear algebra, but they had not been previously applied to GNN training. We show that they can asymptotically reduce communication compared to existing parallel GNN training methods. We implement a promising and practical version that is based on 2D sparse-dense matrix multiplication using torch.distributed. Our implementation parallelizes over GPU-equipped clusters. We train GNNs on up to a hundred GPUs on datasets that include a protein network with over a billion edges.

Motion synthesis in a dynamic environment has been a long-standing problem for character animation. Methods using motion capture data tend to scale poorly in complex environments because of their larger capturing and labeling requirement. Physics-based controllers are effective in this regard, albeit less controllable. In this paper, we present CARL, a quadruped agent that can be controlled with high-level directives and react naturally to dynamic environments. Starting with an agent that can imitate individual animation clips, we use Generative Adversarial Networks to adapt high-level controls, such as speed and heading, to action distributions that correspond to the original animations. Further fine-tuning through the deep reinforcement learning enables the agent to recover from unseen external perturbations while producing smooth transitions. It then becomes straightforward to create autonomous agents in dynamic environments by adding navigation modules over the entire process. We evaluate our approach by measuring the agent's ability to follow user control and provide a visual analysis of the generated motion to show its effectiveness.

The notion of incremental learning is to train an ANN algorithm in stages, as and when newer training data arrives. Incremental learning is becoming widespread in recent times with the advent of deep learning. Noise in the training data reduces the accuracy of the algorithm. In this paper, we make an empirical study of the effect of noise in the training phase. We numerically show that the accuracy of the algorithm is dependent more on the location of the error than the percentage of error. Using Perceptron, Feed Forward Neural Network and Radial Basis Function Neural Network, we show that for the same percentage of error, the accuracy of the algorithm significantly varies with the location of error. Furthermore, our results show that the dependence of the accuracy with the location of error is independent of the algorithm. However, the slope of the degradation curve decreases with more sophisticated algorithms

Restricted Boltzmann Machine (RBM) is an energy based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate exact gradient of log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), which is much faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results are compared with CD. The classification accuracy results indicate similar performance of both methods. Image reconstruction as well as log-likelihood calculations are used to compare the performance of quantum and classical algorithms for RBM training. It is shown that the samples obtained from quantum annealer can be used to train a RBM on a 64-bit `bars and stripes' data set with classification performance similar to a RBM trained with CD. Though training based on CD showed improved learning performance, training using a quantum annealer eliminates computationally expensive MCMC steps of CD.

An accurate and prompt diagnosis of pediatric pneumonia is imperative for successful treatment intervention. One approach to diagnose pneumonia cases is using radiographic data. In this article, we propose a novel parsimonious scalar-on-image classification model adopting the ideas of functional data analysis. Our main idea is to treat images as functional measurements and exploit underlying covariance structures to select basis functions; these bases are then used in approximating both image profiles and corresponding regression coefficient. We re-express the regression model into a standard generalized linear model where the functional principal component scores are treated as covariates. We apply the method to (1) classify pneumonia against healthy and viral against bacterial pneumonia patients, and (2) test the null effect about the association between images and responses. Extensive simulation studies show excellent numerical performance in terms of classification, hypothesis testing, and efficient computation.