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A large set of signals can sometimes be described sparsely using a dictionary, that is, every element can be represented as a linear combination of few elements from the dictionary. Algorithms for various signal processing applications,…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
Generalization error bounds are essential for comprehending how well machine learning models work. In this work, we suggest a novel method, i.e., the Auxiliary Distribution Method, that leads to new upper bounds on expected generalization…
We present a distributed (non-Bayesian) learning algorithm for the problem of parameter estimation with Gaussian noise. The algorithm is expressed as explicit updates on the parameters of the Gaussian beliefs (i.e. means and precision). We…
We explore a supervised machine learning approach to estimate the entanglement entropy of multi-qubit systems from few experimental samples. We put a particular focus on estimating both aleatoric and epistemic uncertainty of the network's…
The problem of least squares regression of a $d$-dimensional unknown parameter is considered. A stochastic gradient descent based algorithm with weighted iterate-averaging that uses a single pass over the data is studied and its convergence…
Existing popular unsupervised embedding learning methods focus on enhancing the instance-level local discrimination of the given unlabeled images by exploring various negative data. However, the existed sample outliers which exhibit large…
We study the basic statistical problem of testing whether normally distributed $n$-dimensional data has been truncated, i.e. altered by only retaining points that lie in some unknown truncation set $S \subseteq \mathbb{R}^n$. As our main…
The problem of network-constrained averaging is to compute the average of a set of values distributed throughout a graph G using an algorithm that can pass messages only along graph edges. We study this problem in the noisy setting, in…
In many learning applications, data are collected from multiple sources, each providing a \emph{batch} of samples that by itself is insufficient to learn its input-output relationship. A common approach assumes that the sources fall in one…
Recent advances in the field of meta-learning have tackled domains consisting of large numbers of small ("few-shot") supervised learning tasks. Meta-learning algorithms must be able to rapidly adapt to any individual few-shot task, fitting…
It is of particular interest to reconstruct or estimate bandlimited graph signals, which are smoothly varying signals defined over graphs, from partial noisy measurements. However, choosing an optimal subset of nodes to sample is NP-hard.…
Sparse inverse covariance estimation (i.e., edge de-tection) is an important research problem in recent years, wherethe goal is to discover the direct connections between a set ofnodes in a networked system based upon the observed…
Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR) as well as a functional…
Inference tasks in signal processing are often characterized by the availability of reliable statistical modeling with some missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and…
We consider the problem of identifying the parameters of an unknown mixture of two arbitrary $d$-dimensional gaussians from a sequence of independent random samples. Our main results are upper and lower bounds giving a computationally…
We propose a novel framework for incorporating unlabeled data into semi-supervised classification problems, where scenarios involving the minimization of either i) adversarially robust or ii) non-robust loss functions have been considered.…
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…
Anomalies are samples that significantly deviate from the rest of the data and their detection plays a major role in building machine learning models that can be reliably used in applications such as data-driven design and novelty…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…