Related papers: Consistency Analysis for the Doubly Stochastic Dir…

Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modelling. Existing methods for uncertainty modelling face a fundamental…

We review some of the properties of higher-dimensional superstatistical stochastic models. As an example, we analyse the stochastic properties of a superstatistical model of 3-dimensional Lagrangian turbulence, and compare with experimental…

Verification is crucial for effective mathematical reasoning. We present a new temporal consistency method where verifiers iteratively refine their judgments based on the previous assessment. Unlike one-round verification or multi-model…

Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…

Decomposing prediction uncertainty into aleatoric (irreducible) and epistemic (reducible) components is critical for the reliable deployment of machine learning systems. While the mutual information between the response variable and model…

This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing…

We introduce a novel varying-weight dependent Dirichlet process (DDP) model that extends a recently developed semi-parametric generalized linear model (SPGLM) by adding a nonparametric Bayesian prior on the baseline distribution of the GLM.…

We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…

The training of machine learning models is typically carried out using some form of gradient descent, often with great success. However, non-asymptotic analyses of first-order optimization algorithms typically employ a gradient smoothness…

Most stochastic gradient descent algorithms can optimize neural networks that are sub-differentiable in their parameters; however, this implies that the neural network's activation function must exhibit a degree of continuity which limits…

Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern datasets where nearby points repel each other. Such…

Multiple clustering has gathered significant attention in recent years due to its potential to reveal multiple hidden structures of the data from different perspectives. Most of multiple clustering methods first derive feature…

We give a new integral characterization of the Dirichlet process on a general phase space. To do so we first prove a characterization of the nonsymmetric Beta distribution via size-biased sampling. Two applications are a new…

Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm in the sequential data setting.…

This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…

In many stochastic models, the observables of interest are naturally encoded in double transforms (e.g., Laplace transforms) that couple spatial and temporal variables. Notably, the double transform often provides the only analytically…

Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using…

We introduce Deep Sigma Point Processes, a class of parametric models inspired by the compositional structure of Deep Gaussian Processes (DGPs). Deep Sigma Point Processes (DSPPs) retain many of the attractive features of (variational)…

Economic policy and research rely on the correct evaluation of the billions of high-frequency data points that we collect every day. Consistent clustering algorithms, like DBSCAN, allow us to make sense of the data in a useful way. However,…

Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. One of the most appealing results within this context are…