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This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…

A fundamental problem in statistical neuroscience is to model how neurons encode information by analyzing electrophysiological recordings. A popular and widely-used approach is to fit the spike trains with an autoregressive point process…

The well-known issue of reconstructing regulatory networks from gene expression measurements has been somewhat disrupted by the emergence and rapid development of single-cell data. Indeed, the traditional way of seeing a gene regulatory…

Analysing non-Gaussian spatial-temporal data requires introducing spatial as well as temporal dependence in generalised linear models through the link function of an exponential family distribution. Unlike in Gaussian likelihoods, inference…

We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…

The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal…

We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard…

A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or…

With the evolution of single-cell RNA sequencing techniques into a standard approach in genomics, it has become possible to conduct cohort-level causal inferences based on single-cell-level measurements. However, the individual gene…

We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…

For more than two centuries, solutions of differential equations have been obtained either analytically or numerically based on typically well-behaved forcing and boundary conditions for well-posed problems. We are changing this paradigm in…

Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…

The episodic, irregular and asynchronous nature of medical data render them difficult substrates for standard machine learning algorithms. We would like to abstract away this difficulty for the class of time-stamped categorical variables…

The focus of this work is the convergence of non-stationary and deep Gaussian process regression. More precisely, we follow a Bayesian approach to regression or interpolation, where the prior placed on the unknown function $f$ is a…

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

Gaussian processes with derivative information are useful in many settings where derivative information is available, including numerous Bayesian optimization and regression tasks that arise in the natural sciences. Incorporating derivative…

Inferring dynamical models from data continues to be a significant challenge in computational biology, especially given the stochastic nature of many biological processes. We explore a common scenario in omics, where statistically…

Learning the kernel parameters for Gaussian processes is often the computational bottleneck in applications such as online learning, Bayesian optimization, or active learning. Amortizing parameter inference over different datasets is a…