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Motivated by stochastic models of climate phenomena, the steady-state of a linear stochastic model with additive Gaussian white noise is studied. Fluctuation theorems for nonequilibrium steady-states provide a constraint on the character of…

We extend observability metrics based on the empirical observability Gramian from deterministic nonlinear systems to nonlinear stochastic systems in order to capture the impact of process noise on observability. We demonstrate that the…

Bayesian active learning relies on the precise quantification of predictive uncertainty to explore unknown function landscapes. While Gaussian process surrogates are the standard for such tasks, an underappreciated fact is that their…

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…

Causal discovery for purely observational, categorical data is a long-standing challenging problem. Unlike continuous data, the vast majority of existing methods for categorical data focus on inferring the Markov equivalence class only,…

Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…

We propose a method for variable selection and basis learning for high-dimensional classification with ordinal responses. The proposed method extends sparse multiclass linear discriminant analysis, with the aim of identifying not only the…

Uncertainty estimation for unlabeled data is crucial to active learning. With a deep neural network employed as the backbone model, the data selection process is highly challenging due to the potential over-confidence of the model…

Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency tables with OTU…

We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…

We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a…

This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational…

We consider a stochastically forced nonlinear oscillator driven by a stationary Gaussian noise that has an algebraically decaying covariance function. It is well known that such noise processes can be renormalized to converge to fractional…

In this paper the solutions $u_{\nu}=u_{\nu}(x,t)$ to fractional diffusion equations of order $0<\nu \leq 2$ are analyzed and interpreted as densities of the composition of various types of stochastic processes. For the fractional equations…

Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…

The paper describes the application of some numerical techniques to analyze and to characterize the observed dynamical behaviour of fluidized bed systems. The preliminary results showed clearly that the dynamics of the considered process…

We present a simple new method for proving that languages are not regular. We prove the correctness of the method, illustrate the ease of using the method on well-known examples of nonregular languages, and prove two additional theorems on…

Optogenetics is a powerful neuroscience technique for studying how neural circuit manipulation affects behavior. Standard analysis conventions discard information and severely limit the scope of the causal questions that can be probed. To…

In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the…