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Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features…

We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity…

Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…

Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…

With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the…

We develop an efficient sampling approach for handling complex missing data patterns and a large number of missing observations in conditionally Gaussian state space models. Two important examples are dynamic factor models with unbalanced…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…

Motivated by recent work involving the analysis of leveraging spatial correlations in sparsified mean estimation, we present a novel procedure for constructing covariance estimator. The proposed Random-knots (Random-knots-Spatial) and…

Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…

In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…

Modeling and computation for multivariate longitudinal surveys have proven challenging, particularly when data are not all continuous and Gaussian but contain discrete measurements. In many social science surveys, study participants are…

Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…

We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…

We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…

Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…

Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…

We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…