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Least squares (LS) fitting is one of the most fundamental techniques in science and engineering. It is used to estimate parameters from multiple noisy observations. In many problems the parameters are known a-priori to be bounded integer…

We propose and analyse a new type of fully discrete finite element approximation of a class of linear stochastic parabolic evolution equations with additive noise. Our discretization differs from previous ones in that we use a finite…

We introduce a simple and linear SNR (strictly speaking, periodic to random power ratio) estimator (0dB to 80dB without additional calibration/linearization) for providing reliable descriptions of aperiodicity in speech corpus. The main…

We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…

Sparse coding strategies have been lauded for their parsimonious representations of data that leverage low dimensional structure. However, inference of these codes typically relies on an optimization procedure with poor computational…

Speech recognition system performance degrades in noisy environments. If the acoustic models are built using features of clean utterances, the features of a noisy test utterance would be acoustically mismatched with the trained model. This…

Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We…

In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and…

AI weather prediction ensembles with latent noise injection and optimized with the continuous ranked probability score (CRPS) have produced both accurate and well-calibrated predictions with far less computational cost compared with…

Distant supervised relation extraction has been successfully applied to large corpus with thousands of relations. However, the inevitable wrong labeling problem by distant supervision will hurt the performance of relation extraction. In…

We present Sequential Neural Likelihood (SNL), a new method for Bayesian inference in simulator models, where the likelihood is intractable but simulating data from the model is possible. SNL trains an autoregressive flow on simulated data…

NOMA) technique based on an algebraic design is studied. We propose an improved low-density spreading (LDS) sequence design based on projective geometry. In terms of its bit error rate (BER) performance, our proposed improved LDS code set…

The SPS-LASSO has recently been introduced as a solution to the problem of regularization parameter selection in the complex-valued LASSO problem. Still, the dependence on the grid size and the polynomial time of performing convex…

This paper is devoted to proving the small noise asymptotic behaviour, particularly large deviation principle, for multi-scale stochastic dynamical systems with fully local monotone coefficients driven by multiplicative noise. The main…

We consider probabilistic model checking for continuous-time Markov chains (CTMCs) induced from Stochastic Reaction Networks (SRNs) against a fragment of Continuous Stochastic Logic (CSL) extended with reward operators. Classical numerical…

We introduce Deep Linear Discriminant Analysis (DeepLDA) which learns linearly separable latent representations in an end-to-end fashion. Classic LDA extracts features which preserve class separability and is used for dimensionality…

Recent research demonstrate that prediction of time series by recurrent neural networks (RNNs) based on the noisy input generates a smooth anticipated trajectory. We examine the internal dynamics of RNNs and establish a set of conditions…

The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…

The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization…

We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by `controlled' Markov noise. In particular, both the faster and slower recursions have non-additive controlled Markov noise…