All Years Seminars
[INMA] 2013-09-11 (14.00) : Rare probability estimation and discrete heavy tails
At Euler building
Speaker :
Mesrob I. Ohannessian (Université Paris-Sud)
Abstract : Despite the increasing volume of data in modern statistical applications, critical patterns and events have often very little,
if any, representation. This isn't unreasonable, given that such variables are critical precisely because they are rare. The natural question is then:
when can we infer something meaningful in such contexts? As a concrete instance of this problem, think of estimating the probability of symbols that
occur very rarely in samples drawn independently from an unknown discrete distribution. The most extreme case is: what is the probability of all
symbols we have never observed? This seems to be ill-posed, yet the classical Good-Turing estimator appears to always work. I will show that, in fact,
if we adopt a multiplicative/relative error notion of consistency, the Good-Turing may fail to be consistent. By taking inspiration from extreme value
theory, I will then demonstrate how a notion of heavy tail is sufficient for consistency. At the core of this result is a new multiplicative
concentration inequality. In the heavy-tailed regime, I will propose new consistent estimators that justify and go beyond some heuristic variants
of the Good-Turing estimator that are used in natural language modeling.
A link to the paper may be found at: http://web.mit.edu/mesrob/www/OhannessianDahleh-COLT2012.pdf
[INMA] 2013-09-03 (14.00) : Minimal Data Rates and Entropy for Control Problems
At Euler building
Speaker :
Kawan, Christoph
Abstract : In the theory of networked control systems, the assumption of classical control theory that information can be transmitted within
control loops instantaneously, lossless, and with arbitrary precision is no longer satisfied. This raises the question about the smallest possible
information rate above which a given control task can be solved. Though networked control systems can have a complicated topology, consisting of
multiple sensors, controllers, and actuators, a first step towards understanding the problem of minimal data rates is to analyze the simplest possible
network topology, consisting of one controller and one dynamical system connected by a digital channel with a certain rate in bits per unit time.
In this setting, the notion of feedback or invariance entropy provides a measure for the minimal data rate associated with the control objective of
rendering a subset of the state space invariant. In my talk, I will explain this concept and present the foundations of a theory which aims at finding
expressions for feedback entropy in terms of dynamical quantities such as Lyapunov exponents.
[INMA] 2013-05-14 (14.00) : The Grid with Intelligent Periphery
At Euler building
Speaker :
Kameshwar Poolla
Abstract : Pressing environmental problems, energy supply security issues, and nuclear power safety concerns drive the worldwide interest
in renewable energy. Renewable energy sources such as wind and solar exhibit variability: they are not dispatchable, exhibit large
fluctuations, and are uncertain. Variability is the most important obstacle to deep integration of renewable generation. The current approach
is to absorbthis variability in operating reserves. This works at todays modest penetration levels. But it will not scale. At deep penetration
levels (>30%) the levels of necessary reserves are economically untenable, and defeat the net carbon benefit.
So how can we economically enable deep penetration of renewable generation? The emerging consensus is that much this new generation must be
placed at hundreds of thousands of locations in the distribution system, and that the attendant variability can be absorbed by the coordinated
aggregation and control of distributed resources such as storage, programmable loads, and smart appliances. Tomorrows grid will have an intelligent
periphery.
We will explore the architectural and algorithmic components for managing this intelligent periphery. Clusters of distributed energy resources
are coordinated to efficiently and reliably offer services (ex: bulk power, regulation) in theface of uncertainty (ex: renewables, consumers).
We begin by formulating a general class of stochastic dynamic programming problems that arise in the context of coordinated aggregation. We then
consider specific real-time scheduling problems for allocating power to resources. We show that no causal optimal policy exists that respects
rate constraints (ex: maximum EV charging rates). Next, we explore the benefits of coordinated aggregation in the metric of operating reserves savings.
We close by suggesting several challenging problems in monetizing and incentivizing resource participation.
[INMA] 2013-05-07 (14.00) : Tensors and graphical models
At Euler building
Speaker :
Ishteva, Mariya
Abstract : In this talk we will discuss existing and new connections between latent variable models from machine learning and tensors (multi-way arrays) from multilinear algebra. A few ideas have been developed independently in the two communities. However, there are still many useful but unexplored links and ideas that could be borrowed from one of the communities and used in the other. We will start our discussion from simple concepts like independent variables and rank-1 matrices and gradually increase the difficulty. The final goal is to connect latent tree graphical models to state of the art tensor decompositions in order to find tractable representations of probability tables of many variables and solve structure learning problems.
Joint work with Le Song and Haesun Park
[INMA] 2013-04-30 (14.00) : Computing tensor decompositions with complex and polynomial optimization
At Euler building
Speaker :
Laurent Sorber (KULeuven)
Abstract : Nonlinear optimization problems in complex variables are frequently encountered in applied mathematics and engineering applications. Tensor decompositions such as the canonical polyadic decomposition are examples of nonlinear optimization problems in several, possibly complex, variables. We give an introduction to tensors and tensor decompositions, their applications and how they can be computed with complex optimization. An important aspect of (complex) optimization are the underlying line and plane search (trust-region) subproblems. We show that in the context of tensor optimization, these subproblems are equivalent to solving a (possibly polyanalytic) polynomial system and develop a robust method of solving such systems with a single generalized eigenvalue decomposition. Finally, algorithms are demonstrated using our recently published MATLAB toolbox Tensorlab.
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