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Time series forecasting is crucial for many fields, such as disaster warning, weather prediction, and energy consumption. The Transformer-based models are considered to have revolutionized the field of sequence modeling. However, the…

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…

Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting…

Most machine learning models operate under the assumption that the training, testing and deployment data is independent and identically distributed (i.i.d.). This assumption doesn't generally hold true in a natural setting. Usually, the…

Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…

Self-Exciting models are statistical models of count data where the probability of an event occurring is influenced by the history of the process. In particular, self-exciting spatio-temporal models allow for spatial dependence as well as…

We consider a stationary linear AR($p$) model with observations subject to gross errors (outliers). The autoregression parameters are unknown as well as the distribution function $G$ of innovations. The distribution of outliers $\Pi$ is…

Statistical methodology for the design and analysis of clinical Phase II dose response studies, with related software implementation, are well developed for the case of a normally distributed, homoscedastic response considered for a single…

We discuss a class of binary parametric families with conditional probabilities taking the form of generalized linear models and show that this approach allows to model high-dimensional random binary vectors with arbitrary mean and…

Probabilistic forecasting consists in predicting a distribution of possible future outcomes. In this paper, we address this problem for non-stationary time series, which is very challenging yet crucially important. We introduce the STRIPE…

We develop a principled way of identifying probability distributions whose independent and identically distributed (iid) realizations are compressible, i.e., can be well-approximated as sparse. We focus on Gaussian random underdetermined…

Multimodal distributions of some physics based model parameters are often encountered in engineering due to different situations such as a change in some environmental conditions, and the presence of some types of damage and nonlinearity.…

We define a class of probability distributions that we call simplicial mixture models, inspired by simplicial complexes from algebraic topology. The parameters of these distributions represent their topology and we show that it is possible…

The use of surrogate models instead of computationally expensive simulation codes is very convenient in engineering. Roughly speaking, there are two kinds of surrogate models: the deterministic and the probabilistic ones. These last are…

We extend the feature selection methodology to dependent data and propose a novel time series predictor selection scheme that accommodates statistical dependence in a more typical i.i.d sub-sampling based framework. Furthermore, the…

This paper extends the subjects dicussed in the Data Analysis and Dynamical Systems courses by looking at the subject of modelling data. This task is nontrivial as the underlying process could be non-linear. In the paper some common…

We propose a flexible model for count time series which has potential uses for both underdispersed and overdispersed data. The model is based on the Conway-Maxwell-Poisson (COM-Poisson) distribution with parameters varying along time to…

Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…

The standard procedures for analysing hierarquical or grouped data are by (non)linear mixed models or generalized mixed models. However, the generalized additive models for location, scale and shape (GAMLSSs) also allow different types of…

In learned image compression, probabilistic models play an essential role in characterizing the distribution of latent variables. The Gaussian model with mean and scale parameters has been widely used for its simplicity and effectiveness.…