Related papers: Stochastic Approximation for High-frequency Observ…

Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…

Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…

Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…

In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…

Large-scale optimization problems are ubiquitous in the physical sciences; yet, high-fidelity models can often be complex and computationally prohibitive for optimization. A practical alternative is to use a low-fidelity model to facilitate…

Multi-time-scale stochastic approximation is an iterative algorithm for finding the fixed point of a set of $N$ coupled operators given their noisy samples. It has been observed that due to the coupling between the decision variables and…

Data augmentation refers to the process of applying a series of transformations or expansions to original data to generate new samples, thereby increasing the diversity and quantity of the data, effectively improving the performance and…

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems…

Informatics and technological advancements have triggered generation of huge volume of data with varied complexity in its management and analysis. Big Data analytics is the practice of revealing hidden aspects of such data and making…

Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data sampling strategies…

Stochastic parameterizations are increasingly being used to represent the uncertainty associated with model errors in ensemble forecasting and data assimilation. One of the challenges associated with the use of these parameterizations is…

In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…

Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…

With ever increasing data rates produced by modern radio telescopes like LOFAR and future telescopes like the SKA, many data processing steps are overwhelmed by the amount of data that needs to be handled using limited compute resources.…

Database theory and database practice are typically the domain of computer scientists who adopt what may be termed an algorithmic perspective on their data. This perspective is very different than the more statistical perspective adopted by…

Errors in the representation of clouds in convection-permitting numerical weather prediction models can be introduced by different sources. These can be the forcing and boundary conditions, the representation of orography, the accuracy of…

This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant…

This paper applies variational data assimilation to inundation problems governed by the shallow water equations with wetting and drying. The objective of the assimilation is to recover an unknown time-varying wave profile at an open ocean…

A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…

As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine…