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In recent years, generative adversarial networks (GANs) have demonstrated impressive experimental results while there are only a few works that foster statistical learning theory for GANs. In this work, we propose an infinite dimensional theoretical framework for generative adversarial learning. Assuming the class of uniformly bounded $k$-times $\alpha$-H\"older differentiable and uniformly positive densities, we show that the Rosenblatt transformation induces an optimal generator, which is realizable in the hypothesis space of $\alpha$-H\"older differentiable generators. With a consistent definition of the hypothesis space of discriminators, we further show that in our framework the Jensen-Shannon divergence between the distribution induced by the generator from the adversarial learning procedure and the data generating distribution converges to zero. Under sufficiently strict regularity assumptions on the density of the data generating process, we also provide rates of convergence based on concentration and chaining.

Many important real-world problems have action spaces that are high-dimensional, continuous or both, making full enumeration of all possible actions infeasible. Instead, only small subsets of actions can be sampled for the purpose of policy evaluation and improvement. In this paper, we propose a general framework to reason in a principled way about policy evaluation and improvement over such sampled action subsets. This sample-based policy iteration framework can in principle be applied to any reinforcement learning algorithm based upon policy iteration. Concretely, we propose Sampled MuZero, an extension of the MuZero algorithm that is able to learn in domains with arbitrarily complex action spaces by planning over sampled actions. We demonstrate this approach on the classical board game of Go and on two continuous control benchmark domains: DeepMind Control Suite and Real-World RL Suite.

To learn intrinsic low-dimensional structures from high-dimensional data that most discriminate between classes, we propose the principle of Maximal Coding Rate Reduction ($\text{MCR}^2$), an information-theoretic measure that maximizes the coding rate difference between the whole dataset and the sum of each individual class. We clarify its relationships with most existing frameworks such as cross-entropy, information bottleneck, information gain, contractive and contrastive learning, and provide theoretical guarantees for learning diverse and discriminative features. The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner. Empirically, the representations learned using this principle alone are significantly more robust to label corruptions in classification than those using cross-entropy, and can lead to state-of-the-art results in clustering mixed data from self-learned invariant features.

Deep reinforcement learning (RL) algorithms have shown an impressive ability to learn complex control policies in high-dimensional environments. However, despite the ever-increasing performance on popular benchmarks such as the Arcade Learning Environment (ALE), policies learned by deep RL algorithms often struggle to generalize when evaluated in remarkably similar environments. In this paper, we assess the generalization capabilities of DQN, one of the most traditional deep RL algorithms in the field. We provide evidence suggesting that DQN overspecializes to the training environment. We comprehensively evaluate the impact of traditional regularization methods, $\ell_2$-regularization and dropout, and of reusing the learned representations to improve the generalization capabilities of DQN. We perform this study using different game modes of Atari 2600 games, a recently introduced modification for the ALE which supports slight variations of the Atari 2600 games traditionally used for benchmarking. Despite regularization being largely underutilized in deep RL, we show that it can, in fact, help DQN learn more general features. These features can then be reused and fine-tuned on similar tasks, considerably improving the sample efficiency of DQN.

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.

Importance sampling is one of the most widely used variance reduction strategies in Monte Carlo rendering. In this paper, we propose a novel importance sampling technique that uses a neural network to learn how to sample from a desired density represented by a set of samples. Our approach considers an existing Monte Carlo rendering algorithm as a black box. During a scene-dependent training phase, we learn to generate samples with a desired density in the primary sample space of the rendering algorithm using maximum likelihood estimation. We leverage a recent neural network architecture that was designed to represent real-valued non-volume preserving ('Real NVP') transformations in high dimensional spaces. We use Real NVP to non-linearly warp primary sample space and obtain desired densities. In addition, Real NVP efficiently computes the determinant of the Jacobian of the warp, which is required to implement the change of integration variables implied by the warp. A main advantage of our approach is that it is agnostic of underlying light transport effects, and can be combined with many existing rendering techniques by treating them as a black box. We show that our approach leads to effective variance reduction in several practical scenarios.

Multispectral imaging is an important technique for improving the readability of written or printed text where the letters have faded, either due to deliberate erasing or simply due to the ravages of time. Often the text can be read simply by looking at individual wavelengths, but in some cases the images need further enhancement to maximise the chances of reading the text. There are many possible enhancement techniques and this paper assesses and compares an extended set of dimensionality reduction methods for image processing. We assess 15 dimensionality reduction methods in two different manuscripts. This assessment was performed both subjectively by asking the opinions of scholars who were experts in the languages used in the manuscripts which of the techniques they preferred and also by using the Davies-Bouldin and Dunn indexes for assessing the quality of the resulted image clusters. We found that the Canonical Variates Analysis (CVA) method which was using a Matlab implementation and we have used previously to enhance multispectral images, it was indeed superior to all the other tested methods. However it is very likely that other approaches will be more suitable in specific circumstance so we would still recommend that a range of these techniques are tried. In particular, CVA is a supervised clustering technique so it requires considerably more user time and effort than a non-supervised technique such as the much more commonly used Principle Component Analysis Approach (PCA). If the results from PCA are adequate to allow a text to be read then the added effort required for CVA may not be justified. For the purposes of comparing the computational times and the image results, a CVA method is also implemented in C programming language and using the GNU (GNUs Not Unix) Scientific Library (GSL) and the OpenCV (OPEN source Computer Vision) computer vision programming library.

Fully convolutional deep neural networks have been asserted to be fast and precise frameworks with great potential in image segmentation. One of the major challenges in utilizing such networks raises when data is unbalanced, which is common in many medical imaging applications such as lesion segmentation where lesion class voxels are often much lower in numbers than non-lesion voxels. A trained network with unbalanced data may make predictions with high precision and low recall, being severely biased towards the non-lesion class which is particularly undesired in medical applications where false negatives are actually more important than false positives. Various methods have been proposed to address this problem including two step training, sample re-weighting, balanced sampling, and similarity loss functions. In this paper we developed a patch-wise 3D densely connected network with an asymmetric loss function, where we used large overlapping image patches for intrinsic and extrinsic data augmentation, a patch selection algorithm, and a patch prediction fusion strategy based on B-spline weighted soft voting to take into account the uncertainty of prediction in patch borders. We applied this method to lesion segmentation based on the MSSEG 2016 and ISBI 2015 challenges, where we achieved average Dice similarity coefficient of 69.9% and 65.74%, respectively. In addition to the proposed loss, we trained our network with focal and generalized Dice loss functions. Significant improvement in $F_1$ and $F_2$ scores and the APR curve was achieved in test using the asymmetric similarity loss layer and our 3D patch prediction fusion. The asymmetric similarity loss based on $F_\beta$ scores generalizes the Dice similarity coefficient and can be effectively used with the patch-wise strategy developed here to train fully convolutional deep neural networks for highly unbalanced image segmentation.

In recent years, person re-identification (re-id) catches great attention in both computer vision community and industry. In this paper, we propose a new framework for person re-identification with a triplet-based deep similarity learning using convolutional neural networks (CNNs). The network is trained with triplet input: two of them have the same class labels and the other one is different. It aims to learn the deep feature representation, with which the distance within the same class is decreased, while the distance between the different classes is increased as much as possible. Moreover, we trained the model jointly on six different datasets, which differs from common practice - one model is just trained on one dataset and tested also on the same one. However, the enormous number of possible triplet data among the large number of training samples makes the training impossible. To address this challenge, a double-sampling scheme is proposed to generate triplets of images as effective as possible. The proposed framework is evaluated on several benchmark datasets. The experimental results show that, our method is effective for the task of person re-identification and it is comparable or even outperforms the state-of-the-art methods.

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in theoretical computer science has shown that, in appropriate distributional models, it is possible to robustly estimate the mean and covariance with polynomial time algorithms that can tolerate a constant fraction of corruptions, independent of the dimension. However, the sample and time complexity of these algorithms is prohibitively large for high-dimensional applications. In this work, we address both of these issues by establishing sample complexity bounds that are optimal, up to logarithmic factors, as well as giving various refinements that allow the algorithms to tolerate a much larger fraction of corruptions. Finally, we show on both synthetic and real data that our algorithms have state-of-the-art performance and suddenly make high-dimensional robust estimation a realistic possibility.