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To scale Gaussian processes (GPs) to large data sets we introduce the robust Bayesian Committee Machine (rBCM), a practical and scalable product-of-experts model for large-scale distributed GP regression. Unlike state-of-the-art sparse GP…
A Gray code for a combinatorial class is a method for listing the objects in the class so that successive objects differ in some prespecified, small way, typically expressed as a bounded Hamming distance. In a previous work, the authors of…
We present the first treatment of the arc length of the Gaussian Process (GP) with more than a single output dimension. GPs are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest.…
We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…
Gaussian sketching, which consists of pre-multiplying the data with a random Gaussian matrix, is a widely used technique for multiple problems in data science and machine learning, with applications spanning computationally efficient…
We present novel, computationally efficient, and differentially private algorithms for two fundamental high-dimensional learning problems: learning a multivariate Gaussian and learning a product distribution over the Boolean hypercube in…
The classical Farey sequence of height $Q$ is the set of rational numbers in reduced form with denominator less than $Q$. In this paper we introduce the concept of a generalized Farey sequence. While these sequences arise naturally in the…
We study a basic private estimation problem: each of $n$ users draws a single i.i.d. sample from an unknown Gaussian distribution, and the goal is to estimate the mean of this Gaussian distribution while satisfying local differential…
We investigate the optimal performance of dense sensor networks by studying the joint source-channel coding problem. The overall goal of the sensor network is to take measurements from an underlying random process, code and transmit those…
Recent results have shown that lattice codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. On the other hand, for Gaussian channels with secrecy constraints, efforts to…
Recent theoretical developments in coset coding theory have provided continuous-valued functions which give the equivocation and maximum likelihood (ML) decoding probability of coset secrecy codes. In this work, we develop a method for…
We uncover a hidden Gaussian ensemble inside each of the three circular ensembles of random matrices, which provide novel diagrammatic rules for the calculation of moments. The matrices involved are generic complex for $\beta=2$, complex…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset $S \subseteq \R^d$. This core problem in truncated statistics has long history going back to…
Motivated by growing concerns over ensuring privacy on social networks, we develop new algorithms and impossibility results for fitting complex statistical models to network data subject to rigorous privacy guarantees. We consider the…
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…
Consider a sequence of bit strings of length d, such that each string differs from the next in a constant number of bits. We call this sequence a quasi-Gray code. We examine the problem of efficiently generating such codes, by considering…
We introduce constrained Gaussian process (CGP), a Gaussian process model for random functions that allows easy placement of mathematical constrains (e.g., non-negativity, monotonicity, etc) on its sample functions. CGP comes with…
Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…