Generalized maximum entropy estimation

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An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

This paper analyzes a class of Stackelberg games where different actors compete for shared resources and a central authority tries to balance the demand through a pricing mechanism. Situations like this can for instance occur when fleet owners of electric ...

We address the numerical solution of the Dirichlet problem for the two-dimensional elliptic Monge-Ampere equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators from the nonlinearitie ...

The HST treasury programme BUFFALO provides extended wide-field imaging of the six Hubble Frontier Fields galaxy clusters. Here we present the combined strong and weak-lensing analysis of Abell 370, a massive cluster at z = 0.375. From the reconstructed to ...

This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

We present a framework for performing regression when both covariate and response are probability distributions on a compact and convex subset of

\R^d

. Our regression model is based on the theory of optimal transport and links the conditional Fr'echet m ...

A kernel method for estimating a probability density function from an independent and identically distributed sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined b ...

One of the most classical results in high-dimensional learning theory provides a closed-form expression for the generalisation error of binary classification with a single-layer teacher-student perceptron on i.i.d. Gaussian inputs. Both Bayes-optimal (BO) ...

This thesis focuses on two selected learning problems: 1) statistical inference on graphs models, and, 2) gradient descent on neural networks, with the common objective of defining and analysing the measures that characterize the fundamental limits. In th ...

Two related methods for inverting line-integrated measurements are presented in this research paper in the context of the recent deuterium-tritium experiments in the JET tokamak. Unlike traditional methods of tomography, these methods rely on making use of ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

Within the context of contemporary machine learning problems, efficiency of optimization process depends on the properties of the model and the nature of the data available, which poses a significant problem as the complexity of either increases ad infinit ...

Forecasting is a capability inherent in humans when navigating. Humans routinely plan their paths, considering the potential future movements of those around them. Similarly, to achieve comparable sophistication and safety, autonomous systems must embrace ...

Quantum random number generators (QRNGs) are a burgeoning technology used for a variety of applications, including modern security and encryption systems. Typical methods exploit an entropy source combined with an extraction or bit generation circuit in or ...

In this paper, we present a spatial branch and bound algorithm to tackle the continuous pricing problem, where demand is captured by an advanced discrete choice model (DCM). Advanced DCMs, like mixed logit or latent class models, are capable of modeling de ...

Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations ...

In this article, we study the problem of Byzantine fault-tolerance in a federated optimization setting, where there is a group of agents communicating with a centralized coordinator. We allow up to

f

Byzantine-faulty agents, which may not follow a prescr ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential models by the MLM ...

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

Generalized maximum entropy estimation

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Results on Sparse Integer Programming and Geometric Independent Sets

On Finding the Leader's Strategy in Quadratic Aggregative Stackelberg Pricing Games

An Adaptive Least-squares Algorithm for the Elliptic Monge-ampere Equation

Beyond the ultradeep frontier fields and legacy observations (BUFFALO): a high-resolution strong plus weak-lensing view of Abell 370

Positive Definite Completions and Continuous Graphical Models

Distributional Regression and Autoregression via Optimal Transport

Density estimation in RKHS with application to Korobov spaces in high dimensions

Learning curves for the multi-class teacher-student perceptron

Fundamental Limits in Statistical Learning Problems: Block Models and Neural Networks

Regressive Tomography and Direct Regressive Reconstruction: A Research Note

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Universal and adaptive methods for robust stochastic optimization

Deep Generative Models for Autonomous Driving: from Motion Forecasting to Realistic Image Synthesis

A 3.3-Gb/s SPAD-Based Quantum Random Number Generator

A Spatial Branch and Bound Algorithm for Continuous Pricing with Advanced Discrete Choice Demand Modeling

Distributionally Robust Linear Quadratic Control

Byzantine Fault-Tolerance in Federated Local SGD Under 2f-Redundancy

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Quantifying uncertain system outputs via the multi-level Monte Carlo method --- distribution and robustness measures

A Functional Perspective on Information Measures