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This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…
In this paper, we investigate Gaussian process regression models where inputs are subject to measurement error. In spatial statistics, input measurement errors occur when the geographical locations of observed data are not known exactly.…
Misspecifications (i.e. errors on the parameters) of state space models lead to incorrect inference of the hidden states. This paper studies weakly nonlin-ear state space models with additive Gaussian noises and proposes a method for…
In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed ``sparse'' noise. In theory, we bound the tracking error. In…
Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…
Most of previous image denoising methods focus on additive white Gaussian noise (AWGN). However,the real-world noisy image denoising problem with the advancing of the computer vision techiniques. In order to promote the study on this…
Pair-wise Markov random fields (MRF) are considered for application to the development of low complexity, iterative MIMO detection. Specifically, we consider two types of MRF, namely, the fully-connected and ring-type. For the edge…
We study the statistical decision process of detecting the signal from a `signal+noise' type matrix model with an additive Wigner noise. We propose a hypothesis test based on the linear spectral statistics of the data matrix, which does not…
We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices. We show that the principal component analysis can be improved by pre-transforming the matrix…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…
We describe a novel approach to the detection and parameter estimation of a non\textendash Gaussian stochastic background of gravitational waves. The method is based on the determination of relevant statistical parameters using importance…
Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…
This paper delves into stochastic optimization problems that involve Markovian noise. We present a unified approach for the theoretical analysis of first-order gradient methods for stochastic optimization and variational inequalities. Our…
Motivated by applications arising in networked systems, this work examines controlled regime-switching systems that stem from a mean-variance formulation. A main point is that the switching process is a hidden Markov chain. An additional…
The problem of estimating a complex measure made up by a linear combination of Dirac distributions centered on points of the complex plane from a finite number of its complex moments affected by additive i.i.d. Gaussian noise is considered.…
We propose a novel deep network architecture for image\\ denoising based on a Gaussian Conditional Random Field (GCRF) model. In contrast to the existing discriminative denoising methods that train a separate model for each noise level, the…
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…
This article considers the application of particle filtering to continuous-discrete optimal filtering problems, where the system model is a stochastic differential equation, and noisy measurements of the system are obtained at discrete…
The problem of detecting changes in the statistical properties of a stochastic system and time series arises in various branches of science and engineering. It has a wide spectrum of important applications ranging from machine monitoring to…
The detection and estimation of signals in noisy, limited data is a problem of interest to many scientific and engineering communities. We present a computationally simple, sample eigenvalue based procedure for estimating the number of…