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We consider online computation of expectations of additive state functionals under general path probability measures proportional to products of unnormalised transition densities. These transition densities are assumed to be intractable but…

The main paradigm of smoothed analysis on graphs suggests that for any large graph $G$ in a certain class of graphs, perturbing slightly the edges of $G$ at random (usually adding few random edges to $G$) typically results in a graph having…

We consider the analysis of continuous repeated measurement outcomes that are collected through time, also known as longitudinal data. A standard framework for analysing data of this kind is a linear Gaussian mixed-effects model within…

We express the classic ARMA time-series model as a directed graphical model. In doing so, we find that the deterministic relationships in the model make it effectively impossible to use the EM algorithm for learning model parameters. To…

Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

There are proposals that extend the classical generalized additive models (GAMs) to accommodate high-dimensional data ($p>>n$) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating…

Tuning hyperparameters, such as the stepsize, presents a major challenge of training machine learning models. To address this challenge, numerous adaptive optimization algorithms have been developed that achieve near-optimal complexities,…

We propose a continuous-time Markov-switching generalized autoregressive conditional heteroskedasticity (COMS-GARCH) process for handling irregularly spaced time series (TS) with multiple volatilities states. We employ a Gibbs sampler in…

We introduce a parsimonious model-based framework for clustering time course data. In these applications the computational burden becomes often an issue due to the number of available observations. The measured time series can also be very…

HYGARCH process is the commonly used long memory process in modeling the long-rang dependence in volatility. Financial time series are characterized by transition between phases of different volatility levels. The smooth transition HYGARCH…

As irregularly structured data representations, graphs have received a large amount of attention in recent years and have been widely applied to various real-world scenarios such as social, traffic, and energy settings. Compared to…

We consider the problem of using experimental time-series data for parameter estimation in nonlinear ordinary differential equations, focusing on the case where the data is noisy, sparse, irregularly sampled, includes multiple experiments,…

Estimating conditional quantiles of financial time series is essential for risk management and many other applications in finance. It is well-known that financial time series display conditional heteroscedasticity. Among the large number of…

Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…

Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…

We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted…

Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…

It is often observed that stochastic gradient descent (SGD) and its variants implicitly select a solution with good generalization performance; such implicit bias is often characterized in terms of the sharpness of the minima. Kleinberg et…

We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…