This paper considers online convex optimization over a complicated constraint set, which typically consists of multiple functional constraints and a set constraint. The conventional online projection algorithm (Zinkevich, 2003) can be difficult to implement due to the potentially high computation complexity of the projection operation. In this paper, we relax the functional constraints by allowing them to be violated at each round but still requiring them to be satisfied in the long term. This type of relaxed online convex optimization (with long term constraints) was first considered in Mahdavi et al. (2012). That prior work proposes an algorithm to achieve $O(sqrt{T})$ regret and $O(T^{3/4})$ constraint violations for general problems and another algorithm to achieve an $O(T^{2/3})$ bound for both regret and constraint violations when the constraint set can be described by a finite number of linear constraints. A recent extension in Jenatton et al. (2016) can achieve $O(T^{max{ heta,1- heta}})$ regret and $O(T^{1- heta/2})$ constraint violations where $ hetain (0,1)$. The current paper proposes a new simple algorithm that yields improved performance in comparison to prior works. The new algorithm achieves an $O(sqrt{T})$ regret bound with $O(1)$ constraint violations.

We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters. We prove finite-sample guarantees on the performance of clustering with respect to this metric when random samples are drawn from multiple intrinsically low-dimensional clusters in high-dimensional space, in the presence of a large number of high-dimensional outliers. By combining these results with spectral clustering with respect to LLPD, we provide conditions under which the Laplacian eigengap statistic correctly determines the number of clusters for a large class of data sets, and prove guarantees on the labeling accuracy of the proposed algorithm. Our methods are quite general and provide performance guarantees for spectral clustering with any ultrametric. We also introduce an efficient, easy to implement approximation algorithm for the LLPD based on a multiscale analysis of adjacency graphs, which allows for the runtime of LLPD spectral clustering to be quasilinear in the number of data points.

We study the least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space as a special case. We first investigate regularized algorithms adapted to a projection operator on a closed subspace of the Hilbert space. We prove convergence results with respect to variants of norms, under a capacity assumption on the hypothesis space and a regularity condition on the target function. As a result, we obtain optimal rates for regularized algorithms with randomized sketches, provided that the sketch dimension is proportional to the effective dimension up to a logarithmic factor. As a byproduct, we obtain similar results for Nystr"{o}m regularized algorithms. Our results provide optimal, distribution-dependent rates that do not have any saturation effect for sketched/Nystr"{o}m regularized algorithms, considering both the attainable and non-attainable cases, in the well-conditioned regimes. We then study stochastic gradient methods with projection over the subspace, allowing multi-pass over the data and minibatches, and we derive similar optimal statistical convergence results.

This paper considers a Bayesian approach to graph-based semi-supervised learning. We show that if the graph parameters are suitably scaled, the graph-posteriors converge to a continuum limit as the size of the unlabeled data set grows. This consistency result has profound algorithmic implications: we prove that when consistency holds, carefully designed Markov chain Monte Carlo algorithms have a uniform spectral gap, independent of the number of unlabeled inputs. Numerical experiments illustrate and complement the theory.

The horseshoe prior is frequently employed in Bayesian analysis of high-dimensional models, and has been shown to achieve minimax optimal risk properties when the truth is sparse. While optimization-based algorithms for the extremely popular Lasso and elastic net procedures can scale to dimension in the hundreds of thousands, algorithms for the horseshoe that use Markov chain Monte Carlo (MCMC) for computation are limited to problems an order of magnitude smaller. This is due to high computational cost per step and growth of the variance of time-averaging estimators as a function of dimension. We propose two new MCMC algorithms for computation in these models that have significantly improved performance compared to existing alternatives. One of the algorithms also approximates an expensive matrix product to give orders of magnitude speedup in high-dimensional applications. We prove guarantees for the accuracy of the approximate algorithm, and show that gradually decreasing the approximation error as the chain extends results in an exact algorithm. The scalability of the algorithm is illustrated in simulations with problem size as large as $N=5,000$ observations and $p=50,000$ predictors, and an application to a genome-wide association study with $N=2,267$ and $p=98,385$. The empirical results also show that the new algorithm yields estimates with lower mean squared error, intervals with better coverage, and elucidates features of the posterior that were often missed by previous algorithms in high dimensions, including bimodality of posterior marginals indicating uncertainty about which covariates belong in the model.

Qianying Liu, Clare A. McGrory, Peter W. J. Baxter.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 2, 267--279.

Abstract:
The pressing need for improved methods for analysing and coping with big data has opened up a new area of research for statisticians. Image analysis is an area where there is typically a very large number of data points to be processed per image, and often multiple images are captured over time. These issues make it challenging to design methodology that is reliable and yet still efficient enough to be of practical use. One promising emerging approach for this problem is to reduce the amount of data that actually has to be processed by extracting what we call coresets from the full dataset; analysis is then based on the coreset rather than the whole dataset. Coresets are representative subsamples of data that are carefully selected via an adaptive sampling approach. We propose a new approach called coreset variational Bayes (CVB) for mixture modelling; this is an algorithm which can perform a variational Bayes analysis of a dataset based on just an extracted coreset of the data. We apply our algorithm to weed image analysis.

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 .

Application and use of deep learning algorithms for different healthcare applications is gaining interest at a steady pace. However, use of such algorithms can prove to be challenging as they require large amounts of training data that capture different possible variations. This makes it difficult to use them in a clinical setting since in most health applications researchers often have to work with limited data. Less data can cause the deep learning model to over-fit. In this paper, we ask how can we use data from a different environment, different use-case, with widely differing data distributions. We exemplify this use case by using single-sensor accelerometer data from healthy subjects performing activities of daily living - ADLs (source dataset), to extract features relevant to multi-sensor accelerometer gait data (target dataset) for Parkinson's disease classification. We train the pre-trained model using the source dataset and use it as a feature extractor. We show that the features extracted for the target dataset can be used to train an effective classification model. Our pre-trained source model consists of a convolutional autoencoder, and the target classification model is a simple multi-layer perceptron model. We explore two different pre-trained source models, trained using different activity groups, and analyze the influence the choice of pre-trained model has over the task of Parkinson's disease classification.

Building a scalable machine learning system for unsupervised anomaly detection via representation learning is highly desirable. One of the prevalent methods is using a reconstruction error from variational autoencoder (VAE) via maximizing the evidence lower bound. We revisit VAE from the perspective of information theory to provide some theoretical foundations on using the reconstruction error, and finally arrive at a simpler and more effective model for anomaly detection. In addition, to enhance the effectiveness of detecting anomalies, we incorporate a practical model uncertainty measure into the metric. We show empirically the competitive performance of our approach on benchmark datasets.

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.

The transfer learning technique is widely used to learning in one context and applying it to another, i.e. the capacity to apply acquired knowledge and skills to new situations. But is it possible to transfer the learning from a deep neural network to a weaker neural network? Is it possible to improve the performance of a weak neural network using the knowledge acquired by a more powerful neural network? In this work, during the training process of a weak network, we add a loss function that minimizes the distance between the features previously learned from a strong neural network with the features that the weak network must try to learn. To demonstrate the effectiveness and robustness of our approach, we conducted a large number of experiments using three known datasets and demonstrated that a weak neural network can increase its performance if its learning process is driven by a more powerful neural network.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Uplift modeling is a predictive modeling technique that estimates the user-level incremental effect of a treatment using machine learning models. It is often used for targeting promotions and advertisements, as well as for the personalization of product offerings. In these applications, there are often hundreds of features available to build such models. Keeping all the features in a model can be costly and inefficient. Feature selection is an essential step in the modeling process for multiple reasons: improving the estimation accuracy by eliminating irrelevant features, accelerating model training and prediction speed, reducing the monitoring and maintenance workload for feature data pipeline, and providing better model interpretation and diagnostics capability. However, feature selection methods for uplift modeling have been rarely discussed in the literature. Although there are various feature selection methods for standard machine learning models, we will demonstrate that those methods are sub-optimal for solving the feature selection problem for uplift modeling. To address this problem, we introduce a set of feature selection methods designed specifically for uplift modeling, including both filter methods and embedded methods. To evaluate the effectiveness of the proposed feature selection methods, we use different uplift models and measure the accuracy of each model with a different number of selected features. We use both synthetic and real data to conduct these experiments. We also implemented the proposed filter methods in an open source Python package (CausalML).

Identification of input data points relevant for the classifier (i.e. serve as the support vector) has recently spurred the interest of researchers for both interpretability as well as dataset debugging. This paper presents an in-depth analysis of the methods which attempt to identify the influence of these data points on the resulting classifier. To quantify the quality of the influence, we curated a set of experiments where we debugged and pruned the dataset based on the influence information obtained from different methods. To do so, we provided the classifier with mislabeled examples that hampered the overall performance. Since the classifier is a combination of both the data and the model, therefore, it is essential to also analyze these influences for the interpretability of deep learning models. Analysis of the results shows that some interpretability methods can detect mislabels better than using a random approach, however, contrary to the claim of these methods, the sample selection based on the training loss showed a superior performance.

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.

We present SmartExchange, an algorithm-hardware co-design framework to trade higher-cost memory storage/access for lower-cost computation, for energy-efficient inference of deep neural networks (DNNs). We develop a novel algorithm to enforce a specially favorable DNN weight structure, where each layerwise weight matrix can be stored as the product of a small basis matrix and a large sparse coefficient matrix whose non-zero elements are all power-of-2. To our best knowledge, this algorithm is the first formulation that integrates three mainstream model compression ideas: sparsification or pruning, decomposition, and quantization, into one unified framework. The resulting sparse and readily-quantized DNN thus enjoys greatly reduced energy consumption in data movement as well as weight storage. On top of that, we further design a dedicated accelerator to fully utilize the SmartExchange-enforced weights to improve both energy efficiency and latency performance. Extensive experiments show that 1) on the algorithm level, SmartExchange outperforms state-of-the-art compression techniques, including merely sparsification or pruning, decomposition, and quantization, in various ablation studies based on nine DNN models and four datasets; and 2) on the hardware level, the proposed SmartExchange based accelerator can improve the energy efficiency by up to 6.7$ imes$ and the speedup by up to 19.2$ imes$ over four state-of-the-art DNN accelerators, when benchmarked on seven DNN models (including four standard DNNs, two compact DNN models, and one segmentation model) and three datasets.

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.

Class imbalance is an inherent characteristic of multi-label data that hinders most multi-label learning methods. One efficient and flexible strategy to deal with this problem is to employ sampling techniques before training a multi-label learning model. Although existing multi-label sampling approaches alleviate the global imbalance of multi-label datasets, it is actually the imbalance level within the local neighbourhood of minority class examples that plays a key role in performance degradation. To address this issue, we propose a novel measure to assess the local label imbalance of multi-label datasets, as well as two multi-label sampling approaches based on the local label imbalance, namely MLSOL and MLUL. By considering all informative labels, MLSOL creates more diverse and better labeled synthetic instances for difficult examples, while MLUL eliminates instances that are harmful to their local region. Experimental results on 13 multi-label datasets demonstrate the effectiveness of the proposed measure and sampling approaches for a variety of evaluation metrics, particularly in the case of an ensemble of classifiers trained on repeated samples of the original data.

Reducing domain divergence is a key step in transfer learning problems. Existing works focus on the minimization of global domain divergence. However, two domains may consist of several shared subdomains, and differ from each other in each subdomain. In this paper, we take the local divergence of subdomains into account in transfer. Specifically, we propose to use low-dimensional manifold to represent subdomain, and align the local data distribution discrepancy in each manifold across domains. A Manifold Maximum Mean Discrepancy (M3D) is developed to measure the local distribution discrepancy in each manifold. We then propose a general framework, called Transfer with Manifolds Discrepancy Alignment (TMDA), to couple the discovery of data manifolds with the minimization of M3D. We instantiate TMDA in the subspace learning case considering both the linear and nonlinear mappings. We also instantiate TMDA in the deep learning framework. Extensive experimental studies demonstrate that TMDA is a promising method for various transfer learning tasks.

People learn to discriminate between classes without explicit exposure to negative examples. On the contrary, traditional machine learning algorithms often rely on negative examples, otherwise the model would be prone to collapse and always-true predictions. Therefore, it is crucial to design the learning objective which leads the model to converge and to perform predictions unbiasedly without explicit negative signals. In this paper, we propose a Collectively loss function to learn from only Positive and Unlabeled data (cPU). We theoretically elicit the loss function from the setting of PU learning. We perform intensive experiments on the benchmark and real-world datasets. The results show that cPU consistently outperforms the current state-of-the-art PU learning methods.

Hierarchical Agglomerative Clustering (HAC) algorithms are extensively utilized in modern data science and machine learning, and seek to partition the dataset into clusters while generating a hierarchical relationship between the data samples themselves. HAC algorithms are employed in a number of applications, such as biology, natural language processing, and recommender systems. Thus, it is imperative to ensure that these algorithms are fair-- even if the dataset contains biases against certain protected groups, the cluster outputs generated should not be discriminatory against samples from any of these groups. However, recent work in clustering fairness has mostly focused on center-based clustering algorithms, such as k-median and k-means clustering. Therefore, in this paper, we propose fair algorithms for performing HAC that enforce fairness constraints 1) irrespective of the distance linkage criteria used, 2) generalize to any natural measures of clustering fairness for HAC, 3) work for multiple protected groups, and 4) have competitive running times to vanilla HAC. To the best of our knowledge, this is the first work that studies fairness for HAC algorithms. We also propose an algorithm with lower asymptotic time complexity than HAC algorithms that can rectify existing HAC outputs and make them subsequently fair as a result. Moreover, we carry out extensive experiments on multiple real-world UCI datasets to demonstrate the working of our algorithms.

Online multiple kernel learning (OMKL) has provided an attractive performance in nonlinear function learning tasks. Leveraging a random feature approximation, the major drawback of OMKL, known as the curse of dimensionality, has been recently alleviated. In this paper, we introduce a new research problem, termed (stream-based) active multiple kernel learning (AMKL), in which a learner is allowed to label selected data from an oracle according to a selection criterion. This is necessary in many real-world applications as acquiring true labels is costly or time-consuming. We prove that AMKL achieves an optimal sublinear regret, implying that the proposed selection criterion indeed avoids unuseful label-requests. Furthermore, we propose AMKL with an adaptive kernel selection (AMKL-AKS) in which irrelevant kernels can be excluded from a kernel dictionary 'on the fly'. This approach can improve the efficiency of active learning as well as the accuracy of a function approximation. Via numerical tests with various real datasets, it is demonstrated that AMKL-AKS yields a similar or better performance than the best-known OMKL, with a smaller number of labeled data.

Current explanation techniques towards a transparent Convolutional Neural Network (CNN) mainly focuses on building connections between the human-understandable input features with models' prediction, overlooking an alternative representation of the input, the frequency components decomposition. In this work, we present an analysis of the connection between the distribution of frequency components in the input dataset and the reasoning process the model learns from the data. We further provide quantification analysis about the contribution of different frequency components toward the model's prediction. We show that the vulnerability of the model against tiny distortions is a result of the model is relying on the high-frequency features, the target features of the adversarial (black and white-box) attackers, to make the prediction. We further show that if the model develops stronger association between the low-frequency component with true labels, the model is more robust, which is the explanation of why adversarially trained models are more robust against tiny distortions.

Crowdsourcing is a popular approach to collect annotations for unlabeled data instances. It involves collecting a large number of annotations from several, often naive untrained annotators for each data instance which are then combined to estimate the ground truth. Further, annotations for constructs such as affect are often multi-dimensional with annotators rating multiple dimensions, such as valence and arousal, for each instance. Most annotation fusion schemes however ignore this aspect and model each dimension separately. In this work we address this by proposing a generative model for multi-dimensional annotation fusion, which models the dimensions jointly leading to more accurate ground truth estimates. The model we propose is applicable to both global and time series annotation fusion problems and treats the ground truth as a latent variable distorted by the annotators. The model parameters are estimated using the Expectation-Maximization algorithm and we evaluate its performance using synthetic data and real emotion corpora as well as on an artificial task with human annotations