# Theory and Algorithms in Data Science

This seminar provides a forum for researchers working in foundational areas of Data Science (and related fields). All talks are held at the Alan Turing Institute. For a complete list of talks held in previous years, please click here.

The organizers are Mihai Cucuringu and Vidit Nanda. We represent the Low-dimensional structure as well as the Topology and geometry research interest groups within the Turing Institute. If you'd like to speak in this seminar, please email Vidit at vnanda@turing.ac.uk

# Upcoming Talks

## 19 Feb 2019: Tengyao Wang, University College London

Speaker : Tengyao Wang, University College London
Title : Isotonic regression in general dimensions

Abstract: We study the least squares regression function estimator over the class of real-valued functions on [0,1]^d that are increasing in each coordinate. For uniformly bounded signals and with a fixed, cubic lattice design, we establish that the estimator achieves the minimax rate of order n^{-min(2/(d+2),1/d)} in the empirical L_2 loss, up to poly-logarithmic factors. Further, we prove a sharp oracle inequality, which reveals in particular that when the true regression function is piecewise constant on k hyperrectangles, the least squares estimator enjoys a faster, adaptive rate of convergence of (k/n)^{min(1,2/d)}, again up to poly-logarithmic factors. Previous results are confined to the case d \leq 2. Finally, we establish corresponding bounds (which are new even in the case d=2) in the more challenging random design setting. There are two surprising features of these results: first, they demonstrate that it is possible for a global empirical risk minimisation procedure to be rate optimal up to poly-logarithmic factors even when the corresponding entropy integral for the function class diverges rapidly; second, they indicate that the adaptation rate for shape-constrained estimators can be strictly worse than the parametric rate.

Room and Time: Augusta, 11h-12h

## 21 Feb 2019: Weining Wang, City, University of London

Speaker : Weining Wang, City, University of London
Title : LASSO-Driven Inference in Time and Space

Abstract: We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak dependence. A sequence of large-scale regressions with LASSO is applied to reduce the dimensionality, and an overall penalty level is carefully chosen by a block multiplier bootstrap procedure to account for multiplicity of the equations and dependencies in the data. Correspondingly, oracle properties with a jointly selected tuning parameter are derived. We further provide high-quality de-biased simultaneous inference on the many target parameters of the system. We provide bootstrap consistency results of the test procedure, which are based on a general Bahadur representation for the $Z$-estimators with dependent data. Simulations demonstrate good performance of the proposed inference procedure. Finally, we apply the method to quantify spillover effects of textual sentiment indices in a financial market and to test the connectedness among sectors.

Room and Time: Augusta, 14h - 15h

## 28 Feb 2019: Seok Young Hong, University of Nottingham

Speaker : Seok Young Hong, University of Nottingham
Title : Nonparametric estimation of infinite order regression and its application to finance.

Abstract: In this walk, we study nonparametric estimation of the infinite order regression with stationary and weakly dependent data. We propose a Nadaraya-Watson type estimator that operates with an infinite number of conditioning variables. We propose a bandwidth sequence that shrinks the effects of long lags, so the influence of all conditioning information is modelled in a natural and flexible way, and the econometric issues of omitted information bias and specification error are effectively handled. We establish the asymptotic properties of the estimator under a wide range of static and dynamic regressions framework, thereby allowing various kinds of conditioning variables to be used. We establish pointwise/uniform consistency and the CLTs. We show that the convergence rates are at best logarithmic, and depend on the smoothness of the regression, the distribution of the marginal regressors and their dependence structure in a non-trivial way via the Lambert W function. As an application, the proposed theory is applied to investigate an important question in finance. We report some new empirical evidence on the dynamics of risk-return relation over time and its link with the macroeconomy, and also add supporting evidence for explaining some major puzzles in finance.

Room and Time: Enigma, 14h-15h

## 12 Mar 2019: Jack Jewson, University of Warwick

Speaker : Jack Jewson, University of Warwick
Title : Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with beta-Divergences

Abstract: We present the first robust Bayesian Online Changepoint Detection algorithm through General Bayesian Inference (GBI) with beta-divergences. The resulting inference procedure is doubly robust for both the parameter and the changepoint (CP) posterior, with linear time and constant space complexity. We provide a construction for exponential models and demonstrate it on the Bayesian Linear Regression model. In so doing, we make two additional contributions: Firstly, we make GBI scalable using Structural Variational approximations that are exact as beta goes to 0. Secondly, we give a principled way of choosing the divergence parameter beta by minimizing expected predictive loss on-line. Reducing False Discovery Rates of CPs from over 90% to 0% on real world data, this offers the state of the art.

Joint work with Jeremias Knoblauch and Theo Damoulas

Room and Time: Enigma, 13h - 14h

## 14 Mar 2019: Ioannis Kosmidis, University of Warwick

Speaker : Ioannis Kosmidis, University of Warwick
Title : TBA

Abstract: TBA

Room and Time: Augusta, 14h - 15h

## 26 Mar 2019: David Barber, University College London

Speaker : David Barber, University College London
Title : TBA

Abstract: TBA

Room and Time: Augusta, 14h - 15h

# Recent Talks

## 14 Feb 2019: Lyudmila Grigoryeva, Universität Konstanz

Speaker : Lyudmila Grigoryeva, Universität Konstanz
Title : Reservoir Computing (RC). Part II: Applicability of RC systems with unbounded inputs and their empirical performance.

Abstract: We show an extension of the results presented in the previous talk to unbounded inputs which is a particularly natural setup for stochastic signals. We complement the universality results with an empirical assessment of performance in applications to time series forecasting. In particular, we focus on predicting financial realized covariance matrices which is a question of much importance for practitioners and researchers. We examine the empirical performance of RC in comparison with many conventional state-of-the-art econometric models for various realized covariance estimators, periods, and dimensions. We show that universal RC families consistently demonstrate superior predictive ability for various empirical designs. We conclude the presentation outlining the work in progress and future lines of research.

Room and Time: Augusta, 14:40h-15:15h

## 14 Feb 2019: Juan-Pablo Ortega, Universität St. Gallen + Centre National de Recherche Scientifique

Speaker : Juan-Pablo Ortega, U St Gallen + CNRS
Title : Reservoir Computing (RC). Part I: RC paradigm and universal approximation properties of RC systems.

Abstract: A relatively recent family of dynamic machine learning paradigms known collectively as reservoir computing is presented which is capable of unprecedented performances in the forecasting of deterministic and stochastic processes. We then focus on the universal approximation properties of the most widely used families of reservoir computers in applications. These results are a much awaited generalization to the dynamic context of previous well-known static results obtained in the context of neural networks. The universal approximation properties with respect to L^\infty and L^p -type criteria of three important families of reservoir computers with stochastic discrete-time semi-infinite inputs are shown. First, it is proved that linear reservoir systems with either polynomial or neural network readout maps are universal. More importantly, it is proved that the same property holds for two families with linear readouts, namely, state-afine systems and echo state networks. The linearity in the readouts is a key feature in supervised machine learning applications. It guarantees that these systems can be used in high-dimensional situations and in the presence of large datasets.

Room and Time: Augusta, 14h - 14:35h

## 07 Feb 2019: Xinghao Qiao, London School of Economics

Speaker : Xinghao Qiao, London School of Economics
Title : A General Theory for Large-Scale Curve Time Series via Functional Stability Measure

Abstract: Modelling a large bundle of curves arises in a broad spectrum of real applications. However, existing literature relies primarily on the critical assumption of independent curve observations. In this talk, we provide a general theory for large-scale Gaussian curve time series, where the temporal and cross-sectional dependence across multiple curve observations exist and the number of functional variables, p, may be large relative to the number of observations, n. We propose a novel functional stability measure for multivariate stationary processes based on their spectral properties and use it to establish some useful concentration bounds on the sample covariance matrix function. These concentration bounds serve as a fundamental tool for further theoretical analysis, in particular, for deriving nonasymptotic upper bounds on the errors of the regularized estimates in high dimensional settings. As functional principle component analysis (FPCA) is one of the key techniques to handle functional data, we also investigate the concentration properties of the relevant estimated terms under a FPCA framework. To illustrate with an important application, we consider vector functional autoregressive models and develop a regularization approach to estimate autoregressive coefficient functions under the sparsity constraint. Using our derived nonasymptotic results, we investigate the theoretical properties of the regularized estimate in a "large p, small n" regime. The finite sample performance of the proposed method is examined through simulation studies.

Room and Time: Augusta, 14h-15h

## 05 Feb 2019: Clifford Lam, London School of Economics

Speaker : Clifford Lam, London School of Economics
Title : Testing for High-Dimensional White Noise

Abstract: Testing for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension p is large in relation to the sample size T, the popular omnibus tests including the multivariate Hosking and Li-McLeod tests are extremely conservative, leading to substantial power loss. To develop more relevant tests for high-dimensional cases, we propose a portmanteau-type test statistic which is the sum of squared singular values of the first q lagged sample autocovariance matrices. It, therefore, encapsulates all the serial correlations (upto the time lag q) within and across all component series. Using the tools from random matrix theory and assuming both p and T diverge to infinity, we derive the asymptotic normality of the test statistic under both the null and a specific VMA(1) alternative hypothesis. As the actual implementation of the test requires the knowledge of three characteristic constants of the population cross-sectional covariance matrix and the value of the fourth moment of the standardized innovations, non-trivial estimations are proposed for these parameters and their integration leads to a practically usable test. Extensive simulation confirms the excellent finite-sample performance of the new test with accurate size and satisfactory power for a large range of finite (p, T) combinations, therefore ensuring wide applicability in practice. We also talk about alternative tests using maximal correlations. Results can be used even for nonlinear processes and non-iid data.

Room and Time: Augusta, 14h-15h

## 29 Jan 2019: Xiaowen Dong, University of Oxford

Speaker : Xiaowen Dong, University of Oxford
Title : Learning Quadratic Games on Networks

Abstract: Individuals, or organisations, cooperate with or compete against one another in a wide range of practical situations. In the economics literature, such strategic interactions are often modelled as games played on networks, where an individual's payoff depends not only on her action but also that of her neighbours. The current literature has largely focused on analysing the characteristics of network games in the scenario where the structure of the network, which is represented by a graph, is known beforehand. It is often the case, however, that the actions of the players are readily observable while the underlying interaction network remains hidden. In this talk, I will introduce two novel frameworks for learning, from the observations on individual actions, network games with linear-quadratic payoffs, and in particular the structure of the interaction network. Both frameworks are based on the Nash equilibrium of such games and involve solving a joint optimisation problem for the graph structure and the individual marginal benefits. We test the proposed frameworks on both synthetic and real world examples, and show that they can effectively and more accurately learn the games than the baselines. The proposed approach has both theoretical and practical implications for understanding strategic interactions in a network environment.

Room and Time: TBA, 14h - 15h