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State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…

Trend filtering is a modern approach to nonparametric regression that is more adaptive to local smoothness than splines or similar basis procedures. Existing analyses of trend filtering focus on estimating a function corrupted by…

Integrating dynamical systems models with time series data is a central part of contemporary mathematical biology. With the rich variety of available models and data, numerous methods and computational tools have been developed for these…

The paper describes the use of Bayesian regression for building time series models and stacking different predictive models for time series. Using Bayesian regression for time series modeling with nonlinear trend was analyzed. This approach…

In this paper it is reconsidered the prediction problem in time series framework by using a new non-parametric approach. Through this reconsideration, the prediction is obtained by a weighted sum of past observed data. These weights are…

We have developed a frequentist approach for model selection which determines the consistency between any cosmological model and the data using the distribution of likelihoods from the iterative smoothing method. Using this approach, we…

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

Despite over three hundred years of effort, no solutions exist for predicting when a general planetary configuration will become unstable. We introduce a deep learning architecture to push forward this problem for compact systems. While…

Since model bias and associated initialization shock are serious shortcomings that reduce prediction skills in state-of-the-art decadal climate prediction efforts, we pursue a complementary machine-learning-based approach to climate…

Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…

Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data…

Recent state-of-the-art forecasting methods are trained on collections of time series. These methods, often referred to as global models, can capture common patterns in different time series to improve their generalization performance.…

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

Delivering precise point and distributional forecasts across a spectrum of prediction horizons represents a significant and enduring challenge in the application of time-series forecasting within various industries. Prior research on…

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…

Extracting meaning from uncertain, noisy data is a fundamental problem across time series analysis, pattern recognition, and language modeling. This survey presents a unified mathematical framework that connects classical estimation theory,…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

Decision-making often involves ranking and selection. For example, to assemble a team of political forecasters, we might begin by narrowing our choice set to the candidates we are confident rank among the top 10% in forecasting ability.…

Bayesian inference methods are applied within a Bayesian hierarchical modelling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple…

The discovery of genomic polymorphisms influencing gene expression (also known as expression quantitative trait loci or eQTLs) can be formulated as a sparse Bayesian multivariate/multiple regression problem. An important aspect in the…