Related papers: Generalized Mixability via Entropic Duality
A common meadow is an enrichment of a field with a partial division operation that is made total by assuming that division by zero takes the a default value, a special element $\bot$ adjoined to the field. To a common meadow of real numbers…
Algorithmic stability is a key characteristic to ensure the generalization ability of a learning algorithm. Among different notions of stability, \emph{uniform stability} is arguably the most popular one, which yields exponential…
We consider general linear non-degenerate weakly-coupled cooperative elliptic systems and study certain monotonicity properties of the generalized principal eigenvalue in $\mathbb{R}^d$ with respect to the potential. It is shown that…
We investigate the problem of online learning, which has gained significant attention in recent years due to its applicability in a wide range of fields from machine learning to game theory. Specifically, we study the online optimization of…
Let $(X,G,\Phi)$ be a dynamical system, where $X$ is compact Hausdorff space, and $G$ is a countable discrete group. We investigate shadowing property and mixing between subshifts and general dynamical systems. For the shadowing property,…
We study online aggregation of the predictions of experts, and first show new second-order regret bounds in the standard setting, which are obtained via a version of the Prod algorithm (and also a version of the polynomially weighted…
The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we…
Recent developments in AI have made it ubiquitous, every industry is trying to adopt some form of intelligent processing of their data. Despite so many advances in the field, AIs full capability is yet to be exploited by the industry.…
In reliability analysis, methods used to estimate failure probability are often limited by the costs associated with model evaluations. Many of these methods, such as multifidelity importance sampling (MFIS), rely upon a computationally…
We show that Optimistic Hedge -- a common variant of multiplicative-weights-updates with recency bias -- attains ${\rm poly}(\log T)$ regret in multi-player general-sum games. In particular, when every player of the game uses Optimistic…
An influential line of recent work has focused on the generalization properties of unregularized gradient-based learning procedures applied to separable linear classification with exponentially-tailed loss functions. The ability of such…
The gain-loss ratio is known to enjoy very good properties from a normative point of view. As a confirmation, we show that the best market gain-loss ratio in the presence of a random endowment is an acceptability index and we provide its…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
We consider learning a convex combination of basis models, and present some new theoretical and empirical results that demonstrate the effectiveness of a greedy approach. Theoretically, we first consider whether we can use linear, instead…
We show that the effectiveness of the well celebrated Mixup [Zhang et al., 2018] can be further improved if instead of using it as the sole learning objective, it is utilized as an additional regularizer to the standard cross-entropy loss.…
We identify a phenomenon, which we refer to as multi-model forgetting, that occurs when sequentially training multiple deep networks with partially-shared parameters; the performance of previously-trained models degrades as one optimizes a…
Large deep neural networks are powerful, but exhibit undesirable behaviors such as memorization and sensitivity to adversarial examples. In this work, we propose mixup, a simple learning principle to alleviate these issues. In essence,…
The push-sum algorithm allows distributed computing of the average on a directed graph, and is particularly relevant when one is restricted to one-way and/or asynchronous communications. We investigate its behavior in the presence of…
Many prediction tasks can admit multiple models that can perform almost equally well. This phenomenon can can undermine interpretability and safety when competing models assign conflicting predictions to individuals. In this work, we study…
We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the…