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Calibration is a common experimental physics problem, whose goal is to infer the value and uncertainty of an unobservable quantity Z given a measured quantity X. Additionally, one would like to quantify the extent to which X and Z are…

The problem of solving linear systems is one of the most fundamental problems in computer science, where given a satisfiable linear system $(A,b)$, for $A \in \mathbb{R}^{n \times n}$ and $b \in \mathbb{R}^n$, we wish to find a vector $x…

Uniform polynomial approximation, also called minimax approximation or Chebyshev approximation, consists in searching polynomial approximation that minimizes the worst case error. Optimality conditions for the uniform approximation of…

We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known…

This paper concerns the problem of matrix completion, which is to estimate a matrix from observations in a small subset of indices. We propose a calibrated spectrum elastic net method with a sum of the nuclear and Frobenius penalties and…

In metric learning, the goal is to learn an embedding so that data points with the same class are close to each other and data points with different classes are far apart. We propose a distance-ratio-based (DR) formulation for metric…

Optimal policies in Markov decision processes (MDPs) are very sensitive to model misspecification. This raises serious concerns about deploying them in high-stake domains. Robust MDPs (RMDP) provide a promising framework to mitigate…

We propose a learning algorithm for cell-load approximation in wireless networks. The proposed algorithm is robust in the sense that it is designed to cope with the uncertainty arising from a small number of training samples. This scenario…

In most (weakly interacting) extensions of the Standard Model the relation mapping the parameter values onto experimentally measurable quantities can be computed (with some uncertainties), but the inverse relation is usually not known. In…

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…

Given pointwise samples of an unknown function belonging to a certain model set, one seeks in Optimal Recovery to recover this function in a way that minimizes the worst-case error of the recovery procedure. While it is often known that…

Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

We present the novel implementation of a non-differentiable metric approximation and a corresponding loss-scheduling aimed at the search for new particles of unknown mass in high energy physics experiments. We call the loss-scheduling,…

In this paper, we present novel deterministic algorithms for multiplying two $n \times n$ matrices approximately. Given two matrices $A,B$ we return a matrix $C'$ which is an \emph{approximation} to $C = AB$. We consider the notion of…

This paper considers the linear objective function optimization with respect to a novel system of fuzzy relation equations, where the fuzzy compositions are defined by the minimum t-norm. It is proved that the feasible solution set is…

Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these models…

We analyse the convergence of an approximate, fully inexact, ADMM algorithm under additive, deterministic and probabilistic error models. We consider the generalized ADMM scheme that is derived from generalized Lagrangian penalty with…

Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of…

We approximate $d$-variate periodic functions in weighted Korobov spaces with general weight parameters using $n$ function values at lattice points. We do not limit $n$ to be a prime number, as in currently available literature, but allow…