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An ensemble method is introduced that utilizes randomization and loss function gradients to compute a prediction. Multiple weakly-correlated estimators approximate the gradient at randomly sampled points on the error surface and are…

We propose a new stochastic optimization framework for empirical risk minimization problems such as those that arise in machine learning. The traditional approaches, such as (mini-batch) stochastic gradient descent (SGD), utilize an…

Beyond minimizing a single training loss, many deep learning estimation pipelines rely on an auxiliary objective to quantify and encourage desirable properties of the model (e.g. performance on another dataset, robustness, agreement with a…

Stochastic Dominance (SD) theory provides a rigorous framework for selecting superior assets tailored to the asset allocation needs of investors with varying risk preferences (i.e., risk-averse, risk-seeking, and risk-neutral). However,…

Data-driven software is increasingly being used as a critical component of automated decision-support systems. Since this class of software learns its logic from historical data, it can encode or amplify discriminatory practices. Previous…

The main goal of this paper is an application of Bayesian inference in testing the relation between risk and return on the financial instruments. On the basis of the Intertemporal CAPM model we built a general sampling model suitable in…

We consider numerical approximations of stochastic differential equations by the Euler method. In the case where the SDE is elliptic or hypoelliptic, we show a weak backward error analysis result in the sense that the generator associated…

Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking. These phenomena appear across architectures -- in…

Quantifying uncertainty about a policy's long-term performance is important to solve sequential decision-making tasks. We study the problem from a model-based Bayesian reinforcement learning perspective, where the goal is to learn the…

Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function…

This paper deals with the estimation of rare event probabilities using importance sampling (IS), where an optimal proposal distribution is computed with the cross-entropy (CE) method. Although, IS optimized with the CE method leads to an…

As data-driven methods are deployed in real-world settings, the processes that generate the observed data will often react to the decisions of the learner. For example, a data source may have some incentive for the algorithm to provide a…

Emotional support conversation (ESC) aims to alleviate distress through empathetic dialogue, yet large language models (LLMs) face persistent challenges in delivering effective ESC due to low accuracy in strategy planning. Moreover, there…

Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…

Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing maximum likelihood estimate when dealing with Gaussian Mixture Model (GMM). When the sample size is smaller than the data dimension, this could lead…

Existing extremum-seeking control (ESC) approaches typically rely on applying repeated perturbations to input parameters and performing measurements of the corresponding performance output. The required separation between the different…

Gradient boosting is a prediction method that iteratively combines weak learners to produce a complex and accurate model. From an optimization point of view, the learning procedure of gradient boosting mimics a gradient descent on a…

We propose two perturbation-based extremum seeking control (ESC) schemes for general single input single output nonlinear dynamical systems, having structures similar to that of the classical ESC scheme. We propose novel adaptation laws for…

Probabilistic forecasts in the form of ensemble of scenarios are required for complex decision making processes. Ensemble forecasting systems provide such products but the spatio-temporal structures of the forecast uncertainty is lost when…

Policy gradient methods are among the most effective methods for large-scale reinforcement learning, and their empirical success has prompted several works that develop the foundation of their global convergence theory. However, prior works…