Related papers: Universal compression of Gaussian sources with unk…
This paper provides a precise error analysis for the maximum likelihood estimate $\hat{a}_{\text{ML}}(u_1^n)$ of the parameter $a$ given samples $u_1^n = (u_1, \ldots, u_n)'$ drawn from a nonstationary Gauss-Markov process $U_i = a U_{i-1}…
We introduce a new decomposition technique for random variables that maps a generic instance of the prophet inequalities problem to a new instance where all but a constant number of variables have a tractable structure that we refer to as…
A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…
Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions with partially overlapping supports. For this class of…
We study asymptotic probabilities of attaining the maximum in heterogeneous Gaussian samples. In the two-group setting, the first sample has variance $1$ and size $n_1$, while the second has variance $\sigma^2>1$ and size $n_2$. We…
Graphical data arises naturally in several modern applications, including but not limited to internet graphs, social networks, genomics and proteomics. The typically large size of graphical data argues for the importance of designing…
Many multivariate data such as social and biological data exhibit complex dependencies that are best characterized by graphs. Unlike sequential data, graphs are, in general, unordered structures. This means we can no longer use classic,…
The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
Reasoning about the pose, i.e. position and orientation of objects is one of the cornerstones of robotic manipulation under uncertainty. In a number of joint research projects our group is developing a robotic perception system that…
The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…
We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an…
Suppose that an infinite lattice gas of constant density $n_0$, whose dynamics are described by the symmetric simple exclusion process, is brought in contact with a spherical absorber of radius $R$. Employing the macroscopic fluctuation…
This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…
The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…
In this work, we propose a novel methodology for robustly estimating particle size distributions from optical scattering measurements using constrained Gaussian process regression. The estimation of particle size distributions is commonly…
We address the problem of finding worst-case nonparametric bounds for T-statistic by considering the extremal problem of maximising the mid-quantile (a special case of 'smoothed quantile' as discussed in \cite{St77} and \cite{W11}) $\tilde…
Slepian-Wolf theorem is a well-known framework that targets almost lossless compression of (two) data streams with symbol-by-symbol correlation between the outputs of (two) distributed sources. However, this paper considers a different…