Sequential Adaptive Detection for In-Situ Transmission Electron Microscopy (TEM)

We develop new efficient online algorithms for detecting transient sparse signals in TEM video sequences, by adopting the recently developed framework for sequential detection jointly with online convex optimization [1]. We cast the problem as detecting an unknown sparse mean shift of Gaussian observations, and develop adaptive CUSUM and adaptive SSRS procedures, which are based on likelihood ratio statistics with post-change mean vector being online maximum likelihood estimators with $\ell_1$. We demonstrate the meritorious performance of our algorithms for TEM imaging using real data

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Stochastic functional descent for learning Support Vector Machines

We present a novel method for learning Support Vector Machines (SVMs) in the online setting. Our method is generally applicable in that it handles the online learning of the binary, multiclass, and structural SVMs in a unified view. The SVM learning problem consists of optimizing a convex objective function that is composed of two parts: the hinge loss and quadratic regularization. To date, the predominant family of approaches for online SVM learning has been gradient-based methods, such as Stochastic Gradient Descent (SGD). Unfortunately, we note that there are two drawbacks in such approaches: first, gradient-based methods are based on a local linear approximation to the function being optimized, but since the hinge loss is piecewise-linear and nonsmooth, this approximation can be ill-behaved. Second, existing online SVM learning approaches share the same problem formulation with batch SVM learning methods, and they all need to tune a fixed global regularization parameter by cross validation. On the one hand, global regularization is ineffective in handling local irregularities encountered in the online setting; on the other hand, even though the learning problem for a particular global regularization parameter value may be efficiently solved, repeatedly solving for a wide range of values can be costly. We intend to tackle these two problems with our approach. To address the first problem, we propose to perform implicit online update steps to optimize the hinge loss, as opposed to explicit (or gradient-based) updates that utilize subgradients to perform local linearization. Regarding the second problem, we propose to enforce local regularization that is applied to individual classifier update steps, rather than having a fixed global regularization term. Our theoretical analysis suggests that our classifier update steps progressively optimize the structured hinge loss, with the rate controlled by a sequence of regularization parameters; setting these parameters is analogous to setting the stepsizes in gradient-based methods. In addition, we give sufficient conditions for the algorithm's convergence. Experimentally, our online algorithm can match optimal classification performances given by other state-of-the-art online SVM learning methods, as well as batch learning methods, after only one or two passes over the training data. More importantly, our algorithm can attain these results without doing cross validation, while all other methods must perform time-consuming cross validation to determine the optimal choice of the global regularization parameter

Sparse Online Learning with Kernels using Random Features for Estimating Nonlinear Dynamic Graphs

Online topology estimation of graph-connected time series is challenging in practice, particularly because the dependencies between the time series in many real-world scenarios are nonlinear. To address this challenge, we introduce a novel kernel-based algorithm for online graph topology estimation. Our proposed algorithm also performs a Fourier-based random feature approximation to tackle the curse of dimensionality associated with kernel representations. Exploiting the fact that real-world networks often exhibit sparse topologies, we propose a group-Lasso based optimization framework, which is solved using an iterative composite objective mirror descent method, yielding an online algorithm with fixed computational complexity per iteration. We provide theoretical guarantees for our algorithm and prove that it can achieve sublinear dynamic regret under certain reasonable assumptions. In experiments conducted on both real and synthetic data, our method outperforms existing state-of-the-art competitors.submittedVersio

Quantum computing for finance

Quantum computers are expected to surpass the computational capabilities of classical computers and have a transformative impact on numerous industry sectors. We present a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on stochastic modeling, optimization, and machine learning. This Review is aimed at physicists, so it outlines the classical techniques used by the financial industry and discusses the potential advantages and limitations of quantum techniques. Finally, we look at the challenges that physicists could help tackle