Related papers: Learning Maximum-A-Posteriori Perturbation Models …

The ability to learn polynomials and generalize out-of-distribution is essential for simulation metamodels in many disciplines of engineering, where the time step updates are described by polynomials. While feed forward neural networks can…

Learning-based approaches to verifying unknown Markov decision processes (MDPs) often employ uncertain MDPs. These models use, for example, confidence intervals to capture transition uncertainty and allow synthesis of policies that are…

We develop a learning-based framework for constructing shrinking disturbance-invariant tubes under state- and input-dependent uncertainty, intended as a building block for tube Model Predictive Control (MPC), and certify safety via a…

The performance of Maximum a posteriori (MAP) estimation is studied analytically for binary symmetric multi-channel Hidden Markov processes. We reduce the estimation problem to a 1D Ising spin model and define order parameters that…

We consider MAP estimators for structured prediction with exponential family models. In particular, we concentrate on the case that efficient algorithms for uniform sampling from the output space exist. We show that under this assumption…

Linguistic representation learning in deep neural language models (LMs) has been studied for decades, for both practical and theoretical reasons. However, finding representations in LMs remains an unsolved problem, in part due to a dilemma…

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…

In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed ``sparse'' noise. In theory, we bound the tracking error. In…

We propose a new method for parameter learning in Bayesian networks with qualitative influences. This method extends our previous work from networks of binary variables to networks of discrete variables with ordered values. The specified…

In applications such as rank aggregation, mixture models for permutations are frequently used when the population exhibits heterogeneity. In this work, we study the widely used Mallows mixture model. In the high-dimensional setting, we…

The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…

Robustness is a key requirement for widespread deployment of machine learning algorithms, and has received much attention in both statistics and computer science. We study a natural model of robustness for high-dimensional statistical…

We present a theory-guided generalized Bayesian methodology for spatio-temporal raster data, which we use to train an ensemble of stochastic feed-forward neural networks with Gaussian-distributed weights. The methodology incorporates the…

We study the task of agnostic learning of multiclass linear classifiers under the Gaussian distribution. Given labeled examples $(x, y)$ from a distribution over $\mathbb{R}^d \times [k]$, with Gaussian $x$-marginal, the goal is to output a…

Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of…

Most of machine learning deals with vector parameters. Ideally we would like to take higher order information into account and make use of matrix or even tensor parameters. However the resulting algorithms are usually inefficient. Here we…

We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative…

A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need to be related back to matrix polynomials. In this paper we…

This work proposes an algorithmic framework to learn time-varying graphs from online data. The generality offered by the framework renders it model-independent, i.e., it can be theoretically analyzed in its abstract formulation and then…

We often use perturbations to regularize neural models. For neural encoder-decoders, previous studies applied the scheduled sampling (Bengio et al., 2015) and adversarial perturbations (Sato et al., 2019) as perturbations but these methods…