Related papers: Fast simulation of truncated Gaussian distribution…
We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector $X$ has finite mean and covariance. In this setting, the radius of confidence intervals achieved…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…
We consider the problem of detecting a change in mean in a sequence of Gaussian vectors. Under the alternative hypothesis, the change occurs only in some subset of the components of the vector. We propose a test of the presence of a…
Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…
We consider the problem of approximating sums of high-dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size $n$,…
It is often the case in Statistics that one needs to compute sums of infinite series, especially in marginalising over discrete latent variables. This has become more relevant with the popularization of gradient-based techniques (e.g.…
In truncated linear regression, samples $(x,y)$ are shown only when the outcome $y$ falls inside a certain survival set $S^\star$ and the goal is to estimate the unknown $d$-dimensional regressor $w^\star$. This problem has a long history…
Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…
We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error…
We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…
Let $X_1, \ldots, X_n\in\mathbb{R}^p$ be i.i.d. random vectors. We aim to perform simultaneous inference for the mean vector $\mathbb{E} (X_i)$ with finite polynomial moments and an ultra high dimension. Our approach is based on the…
We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…
A non trivial problem that arises in several applications is the estimation of the mean of a truncated normal distribution. In this paper, an iterative deterministic scheme for approximating this mean is proposed. It has been inspired from…
We study a distributed estimation problem in which two remotely located parties, Alice and Bob, observe an unlimited number of i.i.d. samples corresponding to two different parts of a random vector. Alice can send $k$ bits on average to…
Support vector machines (SVMs) are an extremely successful type of classification and regression algorithms. Building an SVM entails solving a constrained convex quadratic programming problem, which is quadratic in the number of training…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
In Monte Carlo simulations, proposed configurations are accepted or rejected according to an acceptance ratio, which depends on an underlying probability distribution and an a priori sampling probability. By carefully selecting the…