Data augmentation is a widely used training trick in deep learning to improve the network generalization ability. Despite many encouraging results, several recent studies did point out limitations of the conventional data augmentation scheme in certain scenarios, calling for a better theoretical understanding of data augmentation. In this work, we develop a comprehensive analysis that reveals pros and cons of data augmentation. The main limitation of data augmentation arises from the data bias, i.e. the augmented data distribution can be quite different from the original one. This data bias leads to a suboptimal performance of existing data augmentation methods. To this end, we develop two novel algorithms, termed "AugDrop" and "MixLoss", to correct the data bias in the data augmentation. Our theoretical analysis shows that both algorithms are guaranteed to improve the effect of data augmentation through the bias correction, which is further validated by our empirical studies. Finally, we propose a generic algorithm "WeMix" by combining AugDrop and MixLoss, whose effectiveness is observed from extensive empirical evaluations.

While unsupervised domain translation (UDT) has seen a lot of success recently, we argue that allowing its translation to be mediated via categorical semantic features could enable wider applicability. In particular, we argue that categorical semantics are important when translating between domains with multiple object categories possessing distinctive styles, or even between domains that are simply too different but still share high-level semantics. We propose a method to learn, in an unsupervised manner, categorical semantic features (such as object labels) that are invariant of the source and target domains. We show that conditioning the style of a unsupervised domain translation methods on the learned categorical semantics leads to a considerably better high-level features preservation on tasks such as MNIST$\leftrightarrow$SVHN and to a more realistic stylization on Sketches$\to$Reals.

Federated learning is a distributed optimization paradigm that enables a large number of resource-limited client nodes to cooperatively train a model without data sharing. Several works have analyzed the convergence of federated learning by accounting of data heterogeneity, communication and computation limitations, and partial client participation. However, they assume unbiased client participation, where clients are selected at random or in proportion of their data sizes. In this paper, we present the first convergence analysis of federated optimization for biased client selection strategies, and quantify how the selection bias affects convergence speed. We reveal that biasing client selection towards clients with higher local loss achieves faster error convergence. Using this insight, we propose Power-of-Choice, a communication- and computation-efficient client selection framework that can flexibly span the trade-off between convergence speed and solution bias. Our experiments demonstrate that Power-of-Choice strategies converge up to 3 $\times$ faster and give $10$% higher test accuracy than the baseline random selection.

In this paper, we present a novel approach to approximate the gain function of the feedback particle filter (FPF). The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The numerical problem is to approximate the exact gain function using only finitely many particles sampled from the probability distribution. Inspired by the recent success of the deep learning methods, we represent the gain function as a gradient of the output of a neural network. Thereupon considering a certain variational formulation of the Poisson equation, an optimization problem is posed for learning the weights of the neural network. A stochastic gradient algorithm is described for this purpose. The proposed approach has two significant properties/advantages: (i) The stochastic optimization algorithm allows one to process, in parallel, only a batch of samples (particles) ensuring good scaling properties with the number of particles; (ii) The remarkable representation power of neural networks means that the algorithm is potentially applicable and useful to solve high-dimensional problems. We numerically establish these two properties and provide extensive comparison to the existing approaches.

The goal of this work is to shed light on the remarkable phenomenon of transition to linearity of certain neural networks as their width approaches infinity. We show that the transition to linearity of the model and, equivalently, constancy of the (neural) tangent kernel (NTK) result from the scaling properties of the norm of the Hessian matrix of the network as a function of the network width. We present a general framework for understanding the constancy of the tangent kernel via Hessian scaling applicable to the standard classes of neural networks. Our analysis provides a new perspective on the phenomenon of constant tangent kernel, which is different from the widely accepted "lazy training". Furthermore, we show that the transition to linearity is not a general property of wide neural networks and does not hold when the last layer of the network is non-linear. It is also not necessary for successful optimization by gradient descent.

Replica exchange stochastic gradient Langevin dynamics (reSGLD) has shown promise in accelerating the convergence in non-convex learning; however, an excessively large correction for avoiding biases from noisy energy estimators has limited the potential of the acceleration. To address this issue, we study the variance reduction for noisy energy estimators, which promotes much more effective swaps. Theoretically, we provide a non-asymptotic analysis on the exponential acceleration for the underlying continuous-time Markov jump process; moreover, we consider a generalized Girsanov theorem which includes the change of Poisson measure to overcome the crude discretization based on the Gr\"{o}wall's inequality and yields a much tighter error in the 2-Wasserstein ($\mathcal{W}_2$) distance. Numerically, we conduct extensive experiments and obtain the state-of-the-art results in optimization and uncertainty estimates for synthetic experiments and image data.

A crucial problem in neural networks is to select the most appropriate number of hidden neurons and obtain tight statistical risk bounds. In this work, we present a new perspective towards the bias-variance tradeoff in neural networks. As an alternative to selecting the number of neurons, we theoretically show that $L_1$ regularization can control the generalization error and sparsify the input dimension. In particular, with an appropriate $L_1$ regularization on the output layer, the network can produce a statistical risk that is near minimax optimal. Moreover, an appropriate $L_1$ regularization on the input layer leads to a risk bound that does not involve the input data dimension. Our analysis is based on a new amalgamation of dimension-based and norm-based complexity analysis to bound the generalization error. A consequent observation from our results is that an excessively large number of neurons do not necessarily inflate generalization errors under a suitable regularization.

In machine learning, no data point stands alone. We believe that context is an underappreciated concept in many machine learning methods. We propose Attention-Based Clustering (ABC), a neural architecture based on the attention mechanism, which is designed to learn latent representations that adapt to context within an input set, and which is inherently agnostic to input sizes and number of clusters. By learning a similarity kernel, our method directly combines with any out-of-the-box kernel-based clustering approach. We present competitive results for clustering Omniglot characters and include analytical evidence of the effectiveness of an attention-based approach for clustering.

The decision boundary of a learning algorithm applied to a given task can be viewed as the outcome of a random process: (i) generate a training set and, (ii) apply to it the, potentially randomized, learning algorithm. Recall, see Definitions 4 and 5, that a query-bounded adversary does not know the sample on which the model was trained nor the randomness used by the learner. This means that if the decision boundary has high entropy then the adversary needs to ask many questions to recover the boundary to a high degree of precision. This suggest that high-entropy decision boundaries are robust against query-bounded adversaries since intuitively it is clear that an approximate knowledge of the decision boundary is a prerequisite for a successful attack. Following this reasoning, we present two instances where high entropy of the decision boundary leads to security.

Federated learning enables multiple parties to collaboratively learn a model without exchanging their local data. Currently, federated averaging (FedAvg) is the most widely used federated learning algorithm. However, FedAvg or its variants have obvious shortcomings. It can only be used to learn differentiable models and needs many communication rounds to converge. In this paper, we propose a novel federated learning algorithm FedKT that needs only a single communication round (i.e., round-optimal). With applying the knowledge transfer approach, our algorithm can be applied to any classification model. Moreover, we develop the differentially private versions of FedKT and theoretically analyze the privacy loss. The experiments show that our method can achieve close or better accuracy compared with the other state-of-the-art federated learning algorithms. While the size of training data can influence the machine learning model quality a lot, the data are often dispersed over different parties in reality. Due to regulations on data privacy, the data cannot be centralized to a single party for training. To address these issues, federated learning (Kairouz et al., 2019; Li et al., 2019a;b; Yang et al., 2019) enables multiple parties to collaboratively learn a model without exchanging their local data. It has become a hot research topic and shown promising results in the real world (Bonawitz et al., 2019; Hard et al., 2018; Li et al., 2020a; Peng et al., 2020). Currently, federated averaging (FedAvg) (McMahan et al., 2016) is a widely used federated learning algorithm. Its training is an iterative process with four steps in each iteration. First, the server sends the global model to the selected parties. Second, each of the selected parties updates its model with their local data.