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Fitting a local polynomial model to a noisy sequence of uniformly sampled observations or measurements (i.e. regressing) by minimizing the sum of weighted squared errors (i.e. residuals) may be used to design digital filters for a diverse…

The estimation of the frequencies of multiple superimposed exponentials in noise is an important research problem due to its various applications from engineering to chemistry. In this paper, we propose an efficient and accurate algorithm…

In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…

Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…

In the last decades, due to the huge technological growth observed, it has become increasingly common that a collection of temporal data rapidly accumulates in vast amounts. This provides an opportunity for extracting valuable information…

In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates…

This work considers variational Bayesian inference as an inexpensive and scalable alternative to a fully Bayesian approach in the context of sparsity-promoting priors. In particular, the priors considered arise from scale mixtures of Normal…

Stochastic sampling techniques are ubiquitous in real-time rendering, where performance constraints force the use of low sample counts, leading to noisy intermediate results. To remove this noise, the post-processing step of temporal and…

In the modern age, rankings data is ubiquitous and it is useful for a variety of applications such as recommender systems, multi-object tracking and preference learning. However, most rankings data encountered in the real world is…

Since state-of-the-art uncertainty estimation methods are often computationally demanding, we investigate whether incorporating prior information can improve uncertainty estimates in conventional deep neural networks. Our focus is on…

We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…

Sequential Monte Carlo (SMC), or particle filtering, is a popular class of methods for sampling from an intractable target distribution using a sequence of simpler intermediate distributions. Like other importance sampling-based methods,…

Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…

Although the Bayesian paradigm offers a formal framework for estimating the entire probability distribution over uncertain parameters, its online implementation can be challenging due to high computational costs. We suggest the Adaptive…

Stochastic gradient algorithms are more and more studied since they can deal efficiently and online with large samples in high dimensional spaces. In this paper, we first establish a Central Limit Theorem for these estimates as well as for…

In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) proposed by pitt and shephard (1999). Besides establishing a central limit theorem (CLT) for smoothed particle estimates, we…

We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo…

Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function…

Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…

The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general…