Thursday, September 23, 17:00, room 20.237.
Friedrich Pukelsheim (Universitaet Augsburg)
From Ramon Llull to biproportional representation
Abstract:
The Catalan poet and religious writer Ramon Llull
(1232-1316) was among the first to design a formal
electoral system. We review Llull's work on the
subject, report on our re-discovery of a manuscript of
his that was considered lost, and describe our
electronic edition of Llull's electoral writings, at
"www.uni-augsburg.de/llull". Today's electoral systems
pose different problems originating from the
universality of the suffrage. We present a system of
biproportional representation honoring not only vote
counts that parties win through an election, but also
population counts that geographical districts put
forward based on census data. The system forms part of
the new 2003 electoral law for the Swiss Canton Zurich,
and has been implemented in our Java program BAZI that
is available at "www.uni-augsburg.de/bazi".
Friday, October 22, 17:00, room 20.137.
Paul Switzer (Stanford University)
Trend Decomposition in Multiple Time Series
Abstract:
Regional environmental or meteorological data are commonly available as
parallel time series from multiple monitoring stations. Each of the
station time series embodies aspects of a common smoothly varying
regional time trend, with weights that are specific to each monitoring
location. The regional trends are extracted from the station data by
identifying linear combinations with maximal structure. The
location-specific time-trend coefficients may be regarded as a spatial
field. The interpolated spatial field provides a means for inferring
the time trend at unmonitored locations.
Tuesday, November 2, 13:30, room 20.137.
Gábor Lugosi (UPF)
Regret minimization under partial monitoring.
Abstract:
We consider repeated games in which the player,
instead of observing the action chosen by the opponent in each
game round, receives a feedback generated by the combined choice
of the two players.
We study Hannan consistent players for such games, that is,
randomized playing strategies whose per-round regret vanishes
with probability one as the number $n$ of game rounds goes
to infinity. We prove a general lower bound of $\Omega(n^{-1/3})$
on the convergence rate of the regret, and exhibit a specific
strategy that attains this rate on any game for which a
Hannan consistent player exists.
Joint work with Nicolò Cesa-Bianchi and Gilles Stoltz.
Thursday, November 25, 17:00, room 20.137.
Karl G. Jöreskog (Univesity of Uppsala)
Factor analysis of ordinal variables: BIML vs. FIML
Abstract
Wednesday, December 1, 17:00, room 20.199.
Sarunas Raudys
(Institute of Mathematics and Informatics, Vilnius)
"Two approaches to consider small sample - high dimensionality problems
in pattern recognition."
Abstract: "Statistical" approach supported by C.R.Rao, G. Mc.Lachlan,
A.N. Kolmogorov and plethora of researchers around his laboraty of Statistical
methods in Moscow University and many others are making certain assumptions
about distribution density functions of pattern classes and are deriving
analytical expressions for expected error rates which are rather exact,
however, valid only if the assumptios are correct. In another approach
conditionally represented by V. Vapnik, L.Devroye, G. Lugosgi, S.Amari,
D. Haussler, T. Hastie and others, one makes minimal assumptions and derives
"error" bounds. There exists a certain misunderstanding between supporters of
these two approaches. The speaker in his talk will present a review of
results considered in " S. Raudys and D.Young (2004). Results in statistical
discriminant analysis: A review of the former Soviet Union literature, Journal
of Multivariate Analysis. 89, 1-35", and in this seminar would like to
initiate a discussion around these approaches and utilizations of their
results in practice.
Thursday, December 16, 17:00, room 20.237.
Erika Massimiliani (Universita di Bologna)
"Multidimensional scaling on nonlinear manifolds"
Abstract:
We frequently encounter large sets of high-dimensional data, and the
consequent problem of dimensionality reduction. The problem is, as the
human brain does in everyday perception, to find meaningful low-dimensional
structures hidden in the high-dimensional observation space. Many datasets
have the observed data lying on an embedded submanifold of the high-
dimensional space. The degrees of freedom along this submanifold correspond
to the underlying variables. These datasets may contain nonlinear
structures that are invisible to classical techniques for dimensionality
reduction, such as principal component analysis (PCA) and multidimensional
scaling (MDS). These methods are designed to operate when the submanifold
is embedded linearly, or almost linearly, in the observation space.
More generally there is a wider class of techniques, involving iterative
optimization procedures, by which unsatisfactory linear representations
obtained by PCA or MDS may be improved towards more successful nonlinear
representations of the data. In [1-4] there is a full explanation of new
approaches that are recently devised to address this problem. One of them,
Isomap, attempts to preserve geometry on the manifold, mapping nearby
points on the manifold to nearby points in low-dimensional space, and
distant points to distant points. It is capable of discovering the
nonlinear degrees of freedom that underlie complex natural observations. It
combines the major algorithmic features of PCA and MDS: computational
efficiency, global optimality and asymptotic convergence. The algorithm
works on the idea that only the geodesic distances (in some works called
curvilinear distance) reflect the true low-dimensional geometry of the
manifold.
A lot of new publications [5-8] depend on this algorithm and new
applications [9-10] have been studied. The goal of my research is to
provide empirical evidence of its good performance in different scientific
areas.
References:
[1] J. B. Tenenbaum, V. De Silva and J. C. Langford (2000). A global
geometric framework for nonlinear dimensionality reduction. Science,
290 (5500), 2319-2323.
https://www.sciencemag.org/cgi/reprint/290/5500/2319.pdf
[2] V. de Silva, J. B. Tenenbaum (2002).Global versus local methods
in nonlinear dimensionality reduction. Advances in Neural Information
Processing Systems 15. S. Becker, S., Thrun, S., and Obermayer, K.
(eds). Cambridge, MIT Press, 705-712.
https://web.mit.edu/cocosci/Papers/nips02-localglobal-in-press.pdf
[3] L. Saul and S. Roweis (2002). Think globally, fit locally:
unsupervised learning of low dimensional manifolds. Journal of Machine
Learning Research, 4, 119-155.
https://www.cs.toronto.edu/~roweis/papers/lle_tr02.pdf
[4] S. T. Roweis and L. K. Saul (2000). Nonlinear dimensionality
reduction by locally linear embedding. Science, 290 (5500), 2323-2326.
https://www.sciencemag.org/cgi/reprint/290/5500/2323.pdf
[5] J. A. Lee, A. Lendasse , M. Verleysen (2004). Nonlinear
projection with curvilinear distances: Isomap versus curvilinear
distance analysis. Neurocomputing, 57, 49- 76.
https://www.dice.ucl.ac.be/~verleyse/papers/neurocom04jl.pdf
[6] Y. Bengio, J. Paiement, P. Vincent, O. Delalleau, N. Le Roux, M.
Ouimet (2003). Out-of-Sample Extensions for LLE, Isomap, MDS,
Eigenmaps, and Spectral Clustering. NIPS 2003.
https://www.iro.umontreal.ca/~lisa/pointeurs/tr1238.pdf
[7] J. Nilsson, T. Fioretos, M. H?glund and M. Fontes (2004).
Approximate geodesic distances reveal biologically relevant structures
in microarray data. Bioinformatics, 20 (6), 874-880.
https://lifesciences.asu.edu/bio494/mrosenberg/Nov08-2.pdf
[8] M-H Yang (2002). Extended Isomap for Pattern Classification.
Proceedings of the Eighteenth National Conference on Artificial
Intelligence (AAAI 2002), pp. 224-229,
https://vision.ai.uiuc.edu/mhyang/papers/aaai02.pdf
[9] D. J. Navarro, M. D. Lee (2001). Spatial Visualization of
Document Similarity. Defence Human Factors Special Interest Group
Meeting, 16-17 August, 2001 https://quantrm2.psy.ohio-
state.edu/Navarro/visual.pdf
[10] I. S. Lim, P. H. Ciechomski, S. Sarni, D. Thalmann (2003).
Planar arrangement of High-dimensional Biomedical Data Sets by Isomap
Coordinates. Proceedings of the 16th IEEE Symposium on Computer-Based
Medical Systems (CBMS 2003)
https://ligwww.epfl.ch/Publications/pdf/Lim_and_al_CBMS_03.pdf
Thursday, January 20, 17:00, room 20.137.
Stefan Hoderlein (University of Mannheim)
"Nonparametric Demand Analysis in a Heterogeneous
Population using LPR based Estimators"
Abstracts of the two papers covered in the seminar:
1. This paper is concerned with empirically modelling
the demand behavior of a population with heterogeneous
preferences under a weak conditional independence
assumption. More specifically, we characterize the
testable implications of negative semidefiniteness and
symmetry of the Slutsky matrix across a heterogeneous
population without assuming anything on the functional
form of individual preferences. In the same spirit,
implications of a linear budget set are being
considered.
Since the conditional independence assumption is the
only substantial restriction in this model, we analyze
possible alternatives and solutions if this assumption
is violated. In particular, we consider in detail the
concept of instruments in this framework.
Finally, we provide asymptotic distribution theory for
the new test statistics that emerge out of this
framework, and apply these to Canadian data.
2. In this paper, we introduce a Kernel based
estimation principle for nonparametric models named
local partitioned regression. This principle is a
nonparametric generalization of the familiar partition
regression in linear models. It has several key
advantages:
First, it generates estimators for a very large class
of semi- and nonparametric models. A number of
examples which are particularly relevant for economic
applications will be discussed in this paper. This
class contains the additive, partially linear and
varying coefficient models as well as several other
models that have not been discussed in the literature.
Second, LPR based estimators generally achieve
optimality criteria: They have optimal speed of
convergence and are oracle-efficient. Moreover, they
are simple in structure, widely applicable and
computationally inexpensive.
The LPR estimation principle involves preestimation of
conditional expectations and derivatives of densities.
We establish that the asymptotic distribution of the
estimator remains unaffected by preestimation if the
total number of regressors is smaller than ten, in the
sense that we do not require additional smoothness
assumptions in preestimation. Finally, a Monte-Carlo
simulation underscores these advantages.
Thursday, March 17, 17:00, room 20.179.
Diego Ruiz (UPF)
Some Indexable Families of Restless Bandit Problems
For the abstracts of the two corresponding papers click
here
and here.
Thursday, March 31, 17:00, room 40.041.
Robin Hogarth and Natalia Karelaia (UPF)
Simple models of bounded rationality: Predicting when and why
they are effective
Abstract:
We explore environmental conditions under which simple, boundedly rational
models produce effective responses. Specifically, we derive probabilities
that models identify the best of m alternatives (m > 2) characterized by k
attributes (k > 1). The models include a single variable (lexicographic),
variations of elimination-by-aspects, equal weighting, hybrids of the
preceding, and models exploiting dominance. We compare all with multiple
regression. Four environmental factors affect relative performance: how
attributes are weighted; characteristics of choice sets (e.g., correlational
structure); whether attributes are continuous or binary; and error. We
illustrate the theory with twenty simulated and four empirical datasets.
Fits between predictions and realizations are excellent. No single model is
"best." We further provide an overview by regressing the performance of the
different models on factors characterizing environments. We conclude with
suggestions for further research as well as some economic implications.
Thursday, June 2, 17:00, room 20.137.
Maxwell Stinchcombe
(University of Texas at Austin)
THE UNBEARABLE FLIGHTINESS OF BAYESIANS:
GENERICALLY ERRATIC UPDATING
Abstract:
A decision maker tries to learn the distribution of an observed,
utility relevant, independent and identically distributed (iid) sequence of
random
variables. The random variables have infinite support, and the decision
maker learns by updating their prior distribution on the set of distributions
of the sequence. For a generic set of priors, Bayesian updating and the
corresponding optimizing behavior are wildly erratic.
Thursday, June 16, 17:00, room 20.237.
Nicolas Vayatis
(Université Paris 6)
Recursive aggregation of many classifiers
Abstract:
We consider a recursive algorithm to construct an aggregated estimator
from a finite number of base decision rules in the classification
problem. Similarly to regularized boosting methods, the estimator
approximately minimizes a convex risk functional under the
l1-constraint. It is defined by a stochastic version of the mirror
descent algorithm (i.e., of the method which performs gradient descent
in the dual space) with an additional averaging step. The main result is
an upper bound for the expected accuracy of the proposed estimator. A
similar bound is proved in a more general setting that covers, in
particular, the regression model with squared loss. Eventually, we
present computer simulations which describe the performance of the
method on artificial data and provide a comparison with existing algorithms.
Joint work with A. Juditsky, A. Nazin, and A. Tsybakov.