While deep learning-based classification is generally addressed using standardized approaches, a wide variety of techniques are employed for regression. In computer vision, one particularly popular such technique is that of confidence-based regression, which entails predicting a confidence value for each input-target pair (x,y). While this approach has demonstrated impressive results, it requires important task-dependent design choices, and the predicted confidences often lack a natural probabilistic meaning. We address these issues by proposing Deep Conditional Target Densities (DCTD), a novel and general regression method with a clear probabilistic interpretation. DCTD models the conditional target density p (y x) by using a neural network to directly predict the un-normalized density from (x,y). This model of p (y x) is trained by minimizing the associated negative log-likelihood, approximated using Monte Carlo sampling. We perform comprehensive experiments on four computer vision regression tasks. Our approach outperforms direct regression, as well as other probabilistic and confidence-based methods. Notably, our regression model achieves a 1.9% AP improvement over Faster-RCNN for object detection on the COCO dataset, and sets a new state-of- the-art on visual tracking when applied for bounding box regression. Supervised regression entails learning a model capable of predicting a continuous target value y from an input x, given a set of paired training examples. It is a fundamental machine learning problem with many important applications within computer vision and other domains. While all of these tasks benefit from accurate regression of the target values, high accuracy can even be safety-critical in e.g. automotive and medical applications. Today, such regression problems are commonly tackled using Deep Neural Networks (DNNs), due to their ability to learn powerful feature representations from data. While classification is generally addressed using standardized losses and output representations, a wide variety of different techniques are employed for regression. The most conventional strategy is to train a DNN to directly predict a target y given an input x (Lathuili ere et al., 2019). The training data { (x i,y i)} 2000 i 1 is generated by the ground truth conditional target density p (y x) . DCTD models p (y x) by directly predicting the un-normalized density from the input-target pair (x,y), and is trained by minimizing the associated negative log-likelihood.

Despite the extensive empirical success of deep networks, their o ptimization and generalization properties are still not well understood. Recently, the neural tangent kern el (NTK) has provided the following insight into the problem. In the infinite-width limit, the NTK converges to a limit ing kernel which stays constant during training; on the other hand, when the width is large enough, t he function learned by gradient descent follows the NTK (Jacot et al., 2018). This motivates the study of ov erparameterized networks trained by gradient descent, using properties of the NTK. In fact, paramet ers related to NTK, such as the minimum eigenvalue of the limiting kernel, appear to affect optimization and gen eralization (Arora et al., 2019). However, in addition to such NTK-dependent parameters, prior wo rk also requires the width to depend polynomially on n, 1 /δ or 1 /ǫ, where n denotes the size of the training set, δ denotes the failure probability, and ǫ denotes the target error. These large widths far exceed what is u sed empirically, constituting a significant gap between theory and practice.

Deep learning, through the use of neural networks, has demonstrated remarkable ability to automate many routine tasks when presented with sufficient data for training. The neural network architecture (e.g. number of layers, types of layers, connections between layers, etc.) plays a critical role in determining what, if anything, the neural network is able to learn from the training data. The trend for neural network architectures, especially those trained on ImageNet, has been to grow ever deeper and more complex. The result has been ever increasing accuracy on benchmark datasets with the cost of increased computational demands. In this paper we demonstrate that neural network architectures can be automatically generated, tailored for a specific application, with dual objectives: accuracy of prediction and speed of prediction. Using MENNDL--an HPC-enabled software stack for neural architecture search--we generate a neural network with comparable accuracy to state-of-the-art networks on a cancer pathology dataset that is also $16\times$ faster at inference. The speedup in inference is necessary because of the volume and velocity of cancer pathology data; specifically, the previous state-of-the-art networks are too slow for individual researchers without access to HPC systems to keep pace with the rate of data generation. Our new model enables researchers with modest computational resources to analyze newly generated data faster than it is collected.

Auto-regressive sequence-to-sequence models with attention mechanism have achieved state-of-the-art performance in many tasks such as machine translation and speech synthesis. These models can be difficult to train. The standard approach, teacher forcing, guides a model with reference output history during training. The problem is that the model is unlikely to recover from its mistakes during inference, where the reference output is replaced by generated output. Several approaches deal with this problem, largely by guiding the model with generated output history. To make training stable, these approaches often require a heuristic schedule or an auxiliary classifier. This paper introduces attention forcing, which guides the model with generated output history and reference attention. This approach can train the model to recover from its mistakes, in a stable fashion, without the need for a schedule or a classifier. In addition, it allows the model to generate output sequences aligned with the references, which can be important for cascaded systems like many speech synthesis systems. Experiments on speech synthesis show that attention forcing yields significant performance gain. Experiments on machine translation show that for tasks where various re-orderings of the output are valid, guiding the model with generated output history is challenging, while guiding the model with reference attention is beneficial.

While progress has been made in understanding the robustness of machine learning classifiers to test-time adversaries (evasion attacks), fundamental questions remain unresolved. In this paper, we use optimal transport to characterize the minimum possible loss in an adversarial classification scenario. In this setting, an adversary receives a random labeled example from one of two classes, perturbs the example subject to a neighborhood constraint, and presents the modified example to the classifier. We define an appropriate cost function such that the minimum transportation cost between the distributions of the two classes determines the minimum $0-1$ loss for any classifier. When the classifier comes from a restricted hypothesis class, the optimal transportation cost provides a lower bound. We apply our framework to the case of Gaussian data with norm-bounded adversaries and explicitly show matching bounds for the classification and transport problems as well as the optimality of linear classifiers. We also characterize the sample complexity of learning in this setting, deriving and extending previously known results as a special case. Finally, we use our framework to study the gap between the optimal classification performance possible and that currently achieved by state-of-the-art robustly trained neural networks for datasets of interest, namely, MNIST, Fashion MNIST and CIFAR-10.

Value-based methods constitute a fundamental methodology in planning and deep reinforcement learning (RL). In this paper, we propose to exploit the underlying structures of the state-action value function, i.e., Q function, for both planning and deep RL. In particular, if the underlying system dynamics lead to some global structures of the Q function, one should be capable of inferring the function better by leveraging such structures. Specifically, we investigate the lowrank structure, which widely exists for big data matrices. We verify empirically the existence of low-rank Q functions in the context of control and deep RL tasks (Atari games). As our key contribution, by leveraging Matrix Estimation (ME) techniques, we propose a general framework to exploit the underlying low-rank structure in Q functions, leading to a more efficient planning procedure for classical control, and additionally, a simple scheme that can be applied to any value-based RL techniques to consistently achieve better performance on "low-rank" tasks. Extensive experiments on control tasks and Atari games confirm the efficacy of our approach.

Abstract--Recognizing subtle historical patterns is central to modeling and forecasting problems in time series analysis. Here we introduce and develop a new approach to quantify deviations in the underlying hidden generators of observed data streams, resulting in a new efficiently computable universal metric for time series. The proposed metric is universal in the sense that we can compare and contrast data streams regardless of where and how they are generated, and without any feature engineering step. The approach proposed in this paper is conceptually distinct from our previous work on data smashing [4], and vastly improves discrimination performance and computing speed. The core idea here is the generalization of the notion of KL divergence often used to compare probability distributions to a notion of divergence in time series. We call this the sequence likelihood (SL) divergence, which may be used to measure deviations within a well-defined class of discrete-valued stochastic processes. We devise efficient estimators of SL divergence from finite sample paths, and subsequently formulate a universal metric useful for computing distance between time series produced by hidden stochastic generators. We illustrate the superior performance of the new smash2.0 Pattern disambiguation in two distinct applications involving electroencephalogram data and gait recognition is also illustrated. We are hopeful that the smash2.0 Effi ciently learning stochastic processes is a key challenge in analyzing time-dependency in domains where randomness cannot be ignored. For such learning to occur, we need todefine a distance metric to compare and contrast time series. However these distance metrics mentioned all have either or both of the following limitations: first, dimensionality reduction and feature selection heavily relies on domain knowledge and inevitably incur trade-o ff between precision and computability. Secondly, when dealing with data from nontrivial stochastic process dynamics, state of the art techniques might fail to correctly estimate the similarity or lack thereof between exemplars.

The performance of graph neural nets (GNNs) is known to gradually decrease with increasing number of layers. This decay is partly attributed to oversmoothing, where repeated graph convolutions eventually make node embeddings indistinguishable. We take a closer look at two different interpretations, aiming to quantify oversmoothing. Our main contribution is \method, a novel normalization layer that is based on a careful analysis of the graph convolution operator, which prevents all node embeddings from becoming too similar. What is more, \method is fast, easy to implement without any change to network architecture nor any additional parameters, and is broadly applicable to any GNN. Experiments on real-world graphs demonstrate that \method makes deeper GCN, GAT, and SGC models more robust against oversmoothing, and significantly boosts performance for a new problem setting that benefits from deeper GNNs.

In this paper, we propose a novel implicit semantic data augmentation (ISDA) approach to complement traditional augmentation techniques like flipping, translation or rotation. Our work is motivated by the intriguing property that deep networks are surprisingly good at linearizing features, such that certain directions in the deep feature space correspond to meaningful semantic transformations, e.g., adding sunglasses or changing backgrounds. As a consequence, translating training samples along many semantic directions in the feature space can effectively augment the dataset to improve generalization. To implement this idea effectively and efficiently, we first perform an online estimate of the covariance matrix of deep features for each class, which captures the intra-class semantic variations. Then random vectors are drawn from a zero-mean normal distribution with the estimated covariance to augment the training data in that class. Importantly, instead of augmenting the samples explicitly, we can directly minimize an upper bound of the expected cross-entropy (CE) loss on the augmented training set, leading to a highly efficient algorithm. In fact, we show that the proposed ISDA amounts to minimizing a novel robust CE loss, which adds negligible extra computational cost to a normal training procedure. Although being simple, ISDA consistently improves the generalization performance of popular deep models (ResNets and DenseNets) on a variety of datasets, e.g., CIFAR-10, CIFAR-100 and ImageNet. Code for reproducing our results are available at https://github.com/blackfeather-wang/ISDA-for-Deep-Networks.

We study the accuracy of estimating the covariance and the precision matrix of a $D$-variate sub-Gaussian distribution along a prescribed subspace or direction using the finite sample covariance with $N \geq D$ samples. Our results show that the estimation accuracy depends almost exclusively only on the components of the distribution that correspond to desired subspaces or directions. This is relevant for problems where behavior of data along a lower-dimensional space is of specific interest, such as dimension reduction or structured regression problems. As a by-product of the analysis, we reduce the effect the matrix condition number has on the estimation of precision matrices. Two applications are presented: direction-sensitive eigenspace perturbation bounds, and estimation of the single-index model. For the latter, a new estimator, derived from the analysis, with strong theoretical guarantees and superior numerical performance is proposed.