Research Seminar

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Spring Semester 2017

Note: The highlighted event marks the next occurring event and events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Date / Time Speaker Title Location
28 February 2017
Po-Ling Loh
University of Wisconsin-Madison
Influence maximization in stochastic and adversarial settings  HG  G 19.1 
Abstract: We consider the problem of influence maximization in fixed networks, for both stochastic and adversarial contagion models. In the stochastic setting, nodes are infected in waves according to linear threshold or independent cascade models. We establish upper and lower bounds for the influence of a subset of nodes in the network, where the influence is defined as the expected number of infected nodes at the conclusion of the epidemic. We quantify the gap between our upper and lower bounds in the case of the linear threshold model and illustrate the gains of our upper bounds for independent cascade models in relation to existing results. Importantly, our lower bounds are monotonic and submodular, implying that a greedy algorithm for influence maximization is guaranteed to produce a maximizer within a 1-1/e factor of the truth. In the adversarial setting, an adversary is allowed to specify the edges through which contagion may spread, and the player chooses sets of nodes to infect in successive rounds. We establish upper and lower bounds on the pseudo-regret for possibly stochastic strategies of the adversary and player. This is joint work with Justin Khim and Varun Jog.
7 April 2017
Tommaso Proietti
University of Rome, Tor Vergata
Optimal linear prediction of stochastic trends  HG G 19.1 
Abstract: A recent strand of the time series literature has considered the problem of estimating high-dimensional autocovariance matrices, for the purpose of out of sample prediction. For an integrated time series, the Beveridge-Nelson trend is defined as the current value of the series plus the sum of all forecastable future changes. For the optimal linear projection of all future changes into the space spanned by the past of the series, we need to solve a high-dimensional Toeplitz system involving 𝑛 autocovariances, where 𝑛 is the sample size. The paper proposes a non-parametric estimator of the trend that relies on banding, or tapering, the sample partial autocorrelations, by a regularized Durbin-Levinson algorithm. We derive the properties of the estimator and compare it with alternative parametric estimators based on the direct and indirect finite order autoregressive predictors.
10 April 2017
Shahar Mendelson
Australian National University, Canberra, and Technion, Haifa
The small-ball method and the structure of random coordinate projections   HG G 19.2 
Abstract: We study the geometry of the natural function class extension of a random projection of a subset of $R^d$: for a class of functions $F$ defined on the probability space $(\Omega,\mu)$ and an iid sample X_1,...,X_N with each of the $X_i$'s distributed according to $\mu$, the corresponding coordinate projection of $F$ is the set $\{ (f(X_1),....,f(X_N)) : f \in F\} \subset R^N$. We explain how structural information on such random sets can be derived and then used to address various questions in high dimensional statistics (e.g. regression problems), high dimensional probability (e.g., the extremal singular values of certain random matrices) and high dimensional geometry (e.g., Dvoretzky type theorems). Our focus is on results that are (almost) universally true, with minimal assumptions on the class $F$; these results are established using the recently introduced small-ball method.
10 April 2017
Mladen Kolar
The University of Chicago
Some Recent Advances in Scalable Optimization  HG G 19.2 
Abstract: In this talk, I will present two recent ideas that can help solve large scale optimization problems. In the first part, I will present a method for solving an ell-1 penalized linear and logistic regression problems where data are distributed across many machines. In such a scenario it is computationally expensive to communicate information between machines. Our proposed method requires a small number of rounds of communication to achieve the optimal error bound. Within each round, every machine only communicates a local gradient to the central machine and the central machine solves a ell-1 penalized shifter linear or logistic regression. In the second part, I will discuss usage of sketching as a way to solve linear and logistic regression problems with large sample size and many dimensions. This work is aimed at solving large scale optimization procedures on a single machine, while the extension to a distributed setting is work in progress.
12 May 2017
Walter Distaso
Imperial College
Testing for jump spillovers without testing for jumps  HG G 19.1 
Abstract: The analysis of jumps spillovers across assets and markets is fundamental for risk management and portfolio diversification. This paper develops statistical tools for testing conditional independence among the jump components of the quadratic variation, which are measured as the sum of squared jump sizes over a day. To avoid sequential bias distortion, we do not pretest for the presence of jumps. We proceed in two steps. First, we derive the limiting distribution of the infeasible statistic, based on the unobservable jump component. Second, we provide sufficient conditions for the asymptotic equivalence of the feasible statistic based on realized jumps. When the null is true, and both assets have jumps, the statistic weakly converges to a Gaussian random variable. When instead at least one asset has no jumps, then the statistic approaches zero in probability. We then establish the validity of moon bootstrap critical values. If the null is true and both assets have jumps, both statistics have the same limiting distribution. in the absence of jumps in at least one asset, the bootstrap-based statistic converges to zero at a slower rate. Under the alternative, the bootstrap statistic diverges at a slower rate. Altogether, this means that the use of bootstrap critical values ensures a consistent test with asymptotic size equal to or smaller than alpha. We finally provide an empirical illustration using transactions data on futures and ETFs.
29 June 2017
Victor Chernozhukov
Title T.B.A.  HG G 19.1 
Abstract: tba

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