Incremental learning suffers from two challenging problems; forgetting of old knowledge and intransigence on learning new knowledge. Prediction by the model incrementally learned with a subset of the dataset are thus uncertain and the uncertainty accumulates through the tasks by knowledge transfer. To prevent overfitting to the uncertain knowledge, we propose to penalize confident fitting to the uncertain knowledge by the Maximum Entropy Regularizer (MER). Additionally, to reduce class imbalance and induce a self-paced curriculum on new classes, we exclude a few samples from the new classes in every mini-batch, which we call DropOut Sampling (DOS). We further rethink evaluation metrics for forgetting and intransigence in incremental learning by tracking each sample's confusion at the transition of a task since the existing metrics that compute the difference in accuracy are often misleading. We show that the proposed method, named 'MEDIC', outperforms the state-of-the-art incremental learning algorithms in accuracy, forgetting, and intransigence measured by both the existing and the proposed metrics by a large margin in extensive empirical validations on CIFAR100 and a popular subset of ImageNet dataset (TinyImageNet).

A considerable proportion of research on Bayesian machine learning concerns itself with the fundamental task of inference, developing techniques for an efficient and accurate approximation of the posterior distribution p(θ D) of the model parameters θ conditional on observed data D. However, in most cases, this is not the end goal in itself. Instead, we eventually want to solve a decision problem of some kind and merely use the posterior distribution as a summary of the information provided by the data and the modeling assumptions. For example, we may want to decide to automatically shut down a process to avoid costs associated with its potential failure, yet might not necessarily care about whether we model all aspects of the process accurately. The focus on inference is justified by Bayesian decision theory Berger (1985). It formalizes the notion that the posterior distribution is sufficient for making optimal decisions under a utility. This is achieved by selecting decisions that maximize the expected utility, computed by integrating over the posterior.

We provide a high-dimensional semi-supervised inference framework focused on the mean and variance of the response. Our data are comprised of an extensive set of observations regarding the covariate vectors and a much smaller set of labeled observations where we observe both the response as well as the covariates. We allow the size of the covariates to be much larger than the sample size and impose weak conditions on a statistical form of the data. We provide new estimators of the mean and variance of the response that extend some of the recent results presented in low-dimensional models. In particular, at times we will not necessitate consistent estimation of the functional form of the data. Together with estimation of the population mean and variance, we provide their asymptotic distribution and confidence intervals where we showcase gains in efficiency compared to the sample mean and variance. Our procedure, with minor modifications, is then presented to make important contributions regarding inference about average treatment effects. We also investigate the robustness of estimation and coverage and showcase widespread applicability and generality of the proposed method.

Despite the non-convex nature of their loss functions, deep neural networks are known to generalize well when optimized with stochastic gradient descent (SGD). Recent work conjectures that SGD with proper configuration is able to find wide and flat local minima, which have been proposed to be associated with good generalization performance. In this paper, we observe that local minima of modern deep networks are more than being flat or sharp. Specifically, at a local minimum there exist many asymmetric directions such that the loss increases abruptly along one side, and slowly along the opposite side--we formally define such minima as asymmetric valleys. Under mild assumptions, we prove that for asymmetric valleys, a solution biased towards the flat side generalizes better than the exact minimizer. Further, we show that simply averaging the weights along the SGD trajectory gives rise to such biased solutions implicitly. This provides a theoretical explanation for the intriguing phenomenon observed by Izmailov et al. (2018). In addition, we empirically find that batch normalization (BN) appears to be a major cause for asymmetric valleys.

One of the most common and studied problem in machine learning is classification. While conventional algorithms for supervised classification rely on the determination of a function from features to labels, we propose a different approach based on the estimation of a probabilistic transformation from features to labels. Indeed, we determine a conditional probability distribution of the labels given the features and then features are classified as labels following such distribution. In order to compute the conditional distribution, we follow a robust minimax approach, minimizing the worst-case expectation of the 0-1 loss. By doing so, we find the probabilistic transformation which achieves the minimum risk against an uncertainty set consistent with the training data. We show numerical results obtained by an implementation in python of this method and we compare its performance with state of the art techniques.

How to train a machine learning model while keeping the data private and secure? We present CodedPrivateML, a fast and scalable approach to this critical problem. CodedPrivateML keeps both the data and the model information-theoretically private, while allowing efficient parallelization of training across distributed workers. We characterize CodedPrivateML's privacy threshold and prove its convergence for logistic (and linear) regression. Furthermore, via experiments over Amazon EC2, we demonstrate that CodedPrivateML can provide an order of magnitude speedup (up to $\sim 34\times$) over the state-of-the-art cryptographic approaches.

Linear problems appear in a variety of disciplines and their application for the transmission matrix recovery is one of the most stimulating challenges in biomedical imaging. Its knowledge turns any random media into an optical tool that can focus or transmit an image through disorder. Here, converting an input-output problem into a statistical mechanical formulation, we investigate how inference protocols can learn the transmission couplings by pseudolikelihood maximization. Bridging linear regression and thermodynamics let us propose an innovative framework to pursue the solution of the scattering-riddle. A major interest in biomedical imaging is the comprehension ofthe light scattering through disordered media: many recent studies have achieved light-focusing and image reconstructioneven through complex biological tissues [1,2].

We characterize the effectiveness of a classical algorithm for recovering the Markov graph of a general discrete pairwise graphical model from i.i.d. samples. The algorithm is (appropriately regularized) maximum conditional log-likelihood, which involves solving a convex program for each node; for Ising models this is $\ell_1$-constrained logistic regression, while for more general alphabets an $\ell_{2,1}$ group-norm constraint needs to be used. We show that this algorithm can recover any arbitrary discrete pairwise graphical model, and also characterize its sample complexity as a function of model width, alphabet size, edge parameter accuracy, and the number of variables. We show that along every one of these axes, it matches or improves on all existing results and algorithms for this problem. Our analysis applies a sharp generalization error bound for logistic regression when the weight vector has an $\ell_1$ constraint (or $\ell_{2,1}$ constraint) and the sample vector has an $\ell_{\infty}$ constraint (or $\ell_{2, \infty}$ constraint). We also show that the proposed convex programs can be efficiently solved in $\tilde{O}(n^2)$ running time (where $n$ is the number of variables) under the same statistical guarantees. We provide experimental results to support our analysis.

Existing graph- and hypergraph-based algorithms for document summarization represent the sentences of a corpus as the nodes of a graph or a hypergraph in which the edges represent relationships of lexical similarities between sentences. Each sentence of the corpus is then scored individually, using popular node ranking algorithms, and a summary is produced by extracting highly scored sentences. This approach fails to select a subset of jointly relevant sentences and it may produce redundant summaries that are missing important topics of the corpus. To alleviate this issue, a new hypergraph-based summarizer is proposed in this paper, in which each node is a sentence and each hyperedge is a theme, namely a group of sentences sharing a topic. Themes are weighted in terms of their prominence in the corpus and their relevance to a user-defined query. It is further shown that the problem of identifying a subset of sentences covering the relevant themes of the corpus is equivalent to that of finding a hypergraph transversal in our theme-based hypergraph. Two extensions of the notion of hypergraph transversal are proposed for the purpose of summarization, and polynomial time algorithms building on the theory of submodular functions are proposed for solving the associated discrete optimization problems. The worst-case time complexity of the proposed algorithms is squared in the number of terms, which makes it cheaper than the existing hypergraph-based methods. A thorough comparative analysis with related models on DUC benchmark datasets demonstrates the effectiveness of our approach, which outperforms existing graph- or hypergraph-based methods by at least 6% of ROUGE-SU4 score.

It is known that the Langevin dynamics used in MCMC is the gradient flow of the KL divergence on the Wasserstein space, which helps convergence analysis and inspires recent particle-based variational inference methods (ParVIs). But no more MCMC dynamics is understood in this way. In this work, by developing novel concepts, we propose a theoretical framework that recognizes a general MCMC dynamics as the fiber-gradient Hamiltonian flow on the Wasserstein space of a fiber-Riemannian Poisson manifold. The "conservation + convergence" structure of the flow gives a clear picture on the behavior of general MCMC dynamics. We analyse existing MCMC instances under the framework. The framework also enables ParVI simulation of MCMC dynamics, which enriches the ParVI family with more efficient dynamics, and also adapts ParVI advantages to MCMCs. We develop two ParVI methods for a particular MCMC dynamics and demonstrate the benefits in experiments.