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Bayesian coresets have emerged as a promising approach for implementing scalable Bayesian inference. The Bayesian coreset problem involves selecting a (weighted) subset of the data samples, such that the posterior inference using the…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
In the context of statistical learning, the Information Bottleneck method seeks a right balance between accuracy and generalization capability through a suitable tradeoff between compression complexity, measured by minimum description…
In this paper, we consider the multicollinearity problem in the gamma regression model when model parameters are linearly restricted. The linear restrictions are available from prior information to ensure the validity of scientific theories…
The problem of distributed identification of linear stochastic system with unknown coefficients over time-varying networks is considered. For estimating the unknown coefficients, each agent in the network can only access the input and the…
Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…
The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…
In causal inference, interference occurs when the treatment of one unit may affect the outcomes of other units. The goal of this work is to serve as a guide to the use of linear outcome modeling for estimating causal effects in settings…
The first investigation is made of designs for screening experiments where the response variable is approximated by a generalised linear model. A Bayesian information capacity criterion is defined for the selection of designs that are…
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…
This paper studies the identification of nonlinearly parameterized control systems in given experiments. Several identifiability criteria are established and an implementable algorithm is proposed for practicality with the convergence rate…
This paper studies the convergence rate of a message-passing distributed algorithm for solving a large-scale linear system. This problem is generalised from the celebrated Gaussian Belief Propagation (BP) problem for statistical learning…
This paper proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system.…
Complex dynamic systems can be investigated by fitting mechanistic stochastic dynamic models to time series data. In this context, commonly used Monte Carlo inference procedures for model selection and parameter estimation quickly become…
The interface between stochastic analysis and machine learning is a rapidly evolving field, with path signatures - iterated integrals that provide faithful, hierarchical representations of paths - offering a principled and universal feature…
After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective…
Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…
We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat\'ern correlations whose smoothness parameter $\nu$ is a half-integer. The proposed algorithm only requires $\mathcal{O}(\nu^3 n)$ operations…