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We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy,…
We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The…
Variational methods are attractive for computing Bayesian inference for highly parametrized models and large datasets where exact inference is impractical. They approximate a target distribution - either the posterior or an augmented…
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…
The performance of estimating the common support for jointly sparse signals based on their projections onto lower-dimensional space is analyzed. Support recovery is formulated as a multiple-hypothesis testing problem. Both upper and lower…
Given $d$-dimensional standard Gaussian vectors $\boldsymbol{x}_1,\dots, \boldsymbol{x}_n$, we consider the set of all empirical distributions of its $m$-dimensional projections, for $m$ a fixed constant. Diaconis and Freedman (1984) proved…
Gaussian inference on smooth manifolds is central to robotics, but exact marginalization and conditioning are generally non-Gaussian and geometry-dependent. We study tangent-linearized Gaussian inference and derive explicit non-asymptotic…
Several statistical problems, such as multiple heterogeneous graph analysis, distributed PCA, integrative data analysis, and simultaneous dimension reduction of images, can involve a collection of $m$ matrices whose leading subspaces…
We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…
We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to…
Learning high-dimensional distributions is a significant challenge in machine learning and statistics. Classical research has mostly concentrated on asymptotic analysis of such data under suitable assumptions. While existing works…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used…
In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data.…
Non-gaussian component analysis (NGCA) introduced in offered a method for high dimensional data analysis allowing for identifying a low-dimensional non-Gaussian component of the whole distribution in an iterative and structure adaptive way.…
We study the fundamental tradeoffs between statistical accuracy and computational tractability in the analysis of high dimensional heterogeneous data. As examples, we study sparse Gaussian mixture model, mixture of sparse linear…
Continuous p-dispersion problems with and without boundary constraints are NP-hard optimization problems with numerous real-world applications, notably in facility location and circle packing, which are widely studied in mathematics and…
This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel use of a continuously specified Gaussian random field. We show that for…
The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…
We revisit the problem of robust linear regression under Gaussian covariates with an unknown covariance matrix of condition number $\kappa$. For this fundamental problem, significant gaps remain in our understanding of the trade-offs among…