Department of Statistics & Operations Research
Statistics Seminars
2010/2011
To subscribe to the list, please follow this link
or send email to 12345saharon@post.tau.ac.il54321
(remove numbers unless you are a spammer…)
Second
Semester
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1 March |
Alfred Inselberg, Tel Aviv Univ., Univ. of
Singapore and San Diego SuperComputing Center |
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22 March |
Shulamith Gross, Baruch College |
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29 March |
Dror Kenett, Tel Aviv University |
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12 April |
Gadi Fibich, Tel Aviv University |
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26 April |
Matan Gavish, Stanford
University |
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3 May |
Marina Bogomolov,
Tel Aviv University |
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17 May |
Theofanis
Sapatinas, University of Cyprus |
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24 May |
Ehud Aharoni, IBM Research |
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Generalized Alpha Investing: Definitions, Optimality Results, and
Application to Public Databases |
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31 May |
Ofer Harel, University of
Connecticut |
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Strategies for Data Analysis with Two Types of Missing Values |
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28 June |
Adi Wyner,
The Wharton School, University of Pennsylvania |
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** special summer seminar** |
Uncertainty in 1000 Year Old Reconstructions of the Earth
Temperatures: Criticisms and Rejoinder |
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First
Semester
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12 October |
Yulia Gavrilov |
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19 October |
Danny Feldman, California Institute of
Technology |
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26 October |
Itai
Dattner, |
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2 November |
Ronny Luss, Tel Aviv University |
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16 November |
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Model Selection in Regression: some new (?) thoughts on the old
(?) problem |
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30 November |
Yair Goldberg, University of North
Carolina |
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14 December |
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21 December |
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An Algorithmic Framework for Predicting Side-Effects of Drugs |
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28 December |
Ori Rosen, University of Texas at El Paso |
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4 January |
Noam Shental, Open University |
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Identification of rare alleles and their carriers using
compressed se(que)nsing |
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11 January |
Galit Shmueli, University of Maryland |
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18 January |
Youngjo Lee, |
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Seminars are held on Tuesdays, 10.30 am, Schreiber Building, 309 (see the TAU map ). The seminar organizer is Saharon Rosset.
To join the seminar mailing list or any other inquiries - please call (03)-6408820 or email 12345saharon@post.tau.ac.il54321 (remove numbers unless you are a spammer…)
Seminars from previous years
- 2009-2010
- 2008-2009
- 2007-2008 (organized
by
- 2006-2007
(organized
by
- 2005-2006
(organized
by
- 2004-2005
(organized
by
ABSTRACTS
Peak Detection as Multiple Testing
Abstract: This talk considers the problem of
detecting equal-shaped non-overlapping unimodal peaks
in the presence of Gaussian ergodic stationary noise,
where the number, location and heights of the peaks are unknown. A multiple
testing approach is proposed in which, after kernel smoothing, the presence of
a peak is tested at each observed local maximum. The procedure provides strong
control of the family wise error rate and the false discovery rate
asymptotically as both the signal-to-noise ratio (SNR) and the search space get
large, where the search space may grow exponentially as a function of SNR.
Simulations assuming a Gaussian peak shape and a Gaussian autocorrelation
function show that desired error levels are achieved for relatively low SNR and
are robust to partial peak overlap. Simulations also show that detection power
is maximized when the smoothing bandwidth is close to the bandwidth of the
signal peaks, akin to the well-known matched filter theorem in signal
processing. The procedure is illustrated in an analysis of electrical
recordings of neuronal cell activity.
Core-sets and their applications
Abstract: A coreset
(or, core-set) for a given problem is a "compressed" representation
of its input, in the sense that a solution for the problem with the (small) coreset as input would yield an approximate solution to the
problem with the original (large) input.
This relatively new paradigm implies algorithms that are both provable and
practical for problems in fields such as: Streaming, Compressed Sensing,
Machine learning, Time Series Analysis, Distributed Computing, GPU based
algorithms, and Privacy preserving algorithms.
In this talk, I will present coresets that provide
efficient and provable algorithms for problems such as k-mean/median
clustering, and L_p matrix approximation (known as
PCA/SVD/Linear Regression for p=2) in high-dimensional spaces.
If time permits, we will also construct privacy-preserving coresets
which allow us to answer unbounded number of queries on the dataset without
disclosing information about specific individuals.
This talk is based on papers co-authored with: Amos Fiat, Haim
Kaplan, Michael Langberg, Morteza
Monemizadeh, Kobbi Nissim, Micha Sharir,
Christian Sohler, and David Woodruff
On deconvolution of distribution
functions
Abstract: It is well known that rates of
convergence of estimators in deconvolution problems
are affected by the smoothness of the error density and the density to be estimated.
However, the problem of distribution deconvolution is
more delicate than what was considered so far. We derive different rates of
convergence with respect to the tail behavior of the error characteristic
function. We present optimal in order deconvolution
estimators, both for known and unknown error distribution. An adaptive
estimator which achieves the optimal rates within a logarithmic factor is
developed. Simulation studies comparing the adaptive estimator to other methods
are presented and support the superiority of our method. An example with real
data is also discussed.
Based on joint works with Alexander Goldenshluger
and Benjamin Reiser.
- Ronny
Luss,
Isotonic Recursive Partitioning
Abstract: Isotonic regression is a well-known
nonparametric tool for fitting monotonic data and has been studied from both
theoretical and practical aspects. We
present a new algorithm for isotonic regression based on recursively
partitioning the predictor space through solution of progressively smaller
``best cut'' subproblems. This creates a regularized
sequence of isotonic models of increasing model complexity that converges to
the global isotonic regression solution. The models along the sequence are
often more accurate than the unregularized isotonic
regression model because of the complexity control they offer. We offer
quantification of this complexity control through estimation of degrees of
freedom along the path. We also develop efficient methods for generating the
global solution through this sequence of structured subproblems,
as each subproblem is equivalent to a network flow
problem for which efficient algorithms exist. The success of the regularized
models in prediction and our algorithm's favorable computational properties are
demonstrated through a series of simulated and real data experiments.
This is joint work with Saharon
Rosset and Moni Shahar.
Model Selection in Regression: some new (?) thoughts on the
old (?) problem
Abstract: We discuss the model selection
problem in linear regression, where the number of potential predictors might be
even much larger than the number of observations. The proposed Bayesian approach implies the penalized
least squares estimation with a complexity penalty associated with a prior on
the model size. We present optimality properties of the resulting Bayesian
model selector and compare it with several well-known existing counterparts.
Computational problems and possible solutions will be also discussed.
This is joint work with Vadim Grinshtein
from the Open University.
Q-Learning with Censored Data
Abstract: We develop methodology for a
multistage-decision problem with flexible number of stages in which the rewards
are survival times that are subject to censoring. We present a novel Q-learning
algorithm that is adjusted for censored data and allows a flexible number of
stages. We provide finite sample bounds on the generalization error of the policy
learned by the algorithm, and show that when the optimal Q-functions belong to
the approximation spaces, the expected survival time for policies obtained by
the algorithm converges to that of the optimal policy. We demonstrate the
algorithm's performance using a simulation study.
Analysis of Swimming Sessions Using Semi-Markov Models
Abstract: Detailed monitoring of training
sessions of elite athletes is an important component of their training. In this
talk I will describe an application that performs a precise segmentation and
labeling of swimming sessions. This allows a comprehensive break-down of the
training session, including lap times, detailed statistics of strokes, and
turns. To this end we use semi-Markov models (SMM), a
formalism for labeling and segmenting sequential data. Using the trained
model on test swimming sessions of different swimmers provides highly accurate
segmentation as well as perfect labeling of individual segments.
An Algorithmic Framework for Predicting Side-Effects of
Drugs
Abstract: One of the critical stages in drug
development is the identification of potential side effects for promising drug
leads. Large scale clinical experiments aimed at discovering such side effects
are very costly and may miss subtle or rare side effects. Previous attempts to
systematically predict side effects are sparse and consider each side effect
independently. In this work we report on a novel approach to predict the side
effects of a given drug, taking into consideration information on other drugs
and their side effects. Starting from a query drug, a combination of canonical
correlation analysis and network-based diffusion is applied to predict its side
effects.
We evaluate our method by measuring its performance in a cross validation
setting using a comprehensive data set of 692 drugs and their known side
effects derived from package inserts. For 34% of the drugs the top scoring side
effect matches a known side effect of the drug.
Remarkably, even on unseen data, our method is able to infer side
effects that highly match existing knowledge. In addition, we show that our
method outperforms a prediction scheme that considers each side effect
separately. Our method thus represents a
promising step toward shortcutting the process and reducing the cost of side
effect elucidation.
Adaptive Spectral Estimation for Nonstationary
Time Series
Abstract: We propose methodology for analyzing
possibly nonstationary time series by adaptively
dividing the time series into an unknown but finite number of segments and
estimating the corresponding local spectra by smoothing splines.
The model is formulated in a Bayesian framework, and the estimation relies on
reversible jump Markov chain Monte Carlo (RJMCMC) methods. For a given
segmentation of the times series, the likelihood function is approximated via a
product of local Whittle likelihoods. Thus, no parametric assumption is made
about the process underlying the time series. The number and lengths of the
segments are assumed unknown and may change from one
MCMC iteration to another. The method is illustrated with simulated and real
data.
- Noam Shental, The Open University of
Identification of rare alleles and their carriers using
compressed se(que)nsing
Abstract: Identification of rare variants by resequencing is important both for detecting novel
variations and for screening individuals for known disease alleles. New
technologies enable low-cost resequencing of target
regions, although it is still prohibitive to test more than a few individuals.
We propose a novel pooling design that enables the recovery of novel or known
rare alleles and their carriers in groups of individuals. The method is based
on a Compressed Sensing (CS) approach, which is general, simple and efficient.
CS allows the use of generic algorithmic tools for simultaneous identification
of multiple variants and their carriers. We model the experimental procedure
and show via computer simulations that it enables the recovery of rare alleles
and their carriers in larger groups than were possible before. Our approach can
also be combined with barcoding techniques to provide
a feasible solution based on current resequencing
costs. For example, when targeting a small enough genomic region (~100 bp) and using only ~10 sequencing lanes and ~10 distinct
barcodes per lane, one recovers the identity of 4 rare allele carriers out of a
population of over 4000 individuals. We demonstrate the performance of our
approach over several publicly available experimental data sets, including the
1000 Genomes Pilot 3 study.
We believe our approach may significantly improve cost effectiveness in future
Association Studies, and in screening large DNA cohorts for specific risk
alleles.
Joint work with Amnon Amir from the Weizmann
Institute of Science, and Or Zuk from the Broad
Institute of MIT and Harvard
COM-Poisson
Regression: A Flexible Model for Count Data
Abstract:
Poisson regression is a popular tool for modeling count data and is applied in
a vast array of applications from the social to the physical sciences and
beyond. Real data, however, are often over- or under-dispersed and, thus, not
conducive to Poisson regression. We propose a regression model based on the
Conway–Maxwell-Poisson (COM-Poisson) distribution to address this problem. The
COM-Poisson regression generalizes the well-known Poisson and logistic
regression models, and is suitable for fitting count data with a wide range of
dispersion levels. With a GLM approach that takes advantage of exponential
family properties, we discuss model estimation, inference, diagnostics, and
interpretation, and present a test for determining the need for a COM-Poisson
regression over a standard Poisson regression. We compare the COM-Poisson to
several alternatives and illustrate its advantages and usefulness on data sets
with varying dispersion levels.
Joint with Kim Sellers, Georgetown
University
- Youngjo Lee,
Likelihood approach to large-scale
multiple testing
Abstract: To date, only frequentistic,
Bayesian and empirical Bayes approaches have been
studied for the large-scale inference problem of testing simultaneously
hundreds or thousands of hypotheses. One consequence has been the need to
consider an empirical null distribution in order to avoid the problem of
rejection of all null hypotheses when sample sizes are large. We present the
multiple testing problem as a multiple prediction
problem of whether a null hypothesis is true or not. We introduce a hierarchical random-effect models and show how the
extended likelihood is build. It is shown that the maximum likelihood
prediction has a certain oracle property. The extended likelihood leads to new
testing procedures, which are optimal for the usual loss function in hypothesis
testing. The new tests control the local probability of false discovery for
individual tests to maintain false discovery rate globally. One advantage with
this likelihood approach is that there is no need to consider an empirical null
distribution. Several examples are considered to show how to use the likelihood
method in practice.
Visualization & Data Mining for High Dimensional Data
Abstract: A dataset with M items has 2M
subsets anyone of which may be the one satisfying our objectives. With a good
data display and interactivity our fantastic pattern-recognition can not only
cut great swaths searching through this combinatorial explosion, but also
extract insights from the visual patterns. These are the core reasons for data
visualization. With parallel coordinates the search for relations in
multivariate datasets is transformed into a 2-D pattern recognition problem.
Guidelines and strategies for knowledge discovery are illustrated on several
real datasets (financial, process control, credit-score, intrusion-detection
etc) one with hundreds of variables. A geometric classification algorithm is
presented and applied to complex datasets. It has low computational complexity
providing the classification rule explicitly and visually. The minimal set of
variables required to state the rule (features) is found and ordered by their
predictive value. Multivariate relations can be modeled as hypersurfaces
and used for decision support. A model of a (real) country’s economy reveals sensitivies, impact of constraints, trade-offs and economic
sectors unknowingly competing for the same resources. An overview of the
methodology provides foundational understanding; learning the patterns
corresponding to various multivariate relations. These patterns are robust in
the presence of errors and that is good news for the applications.
The parallel coordinates methodology has been applied
to collision avoidance and conflict resolution algorithms for air traffic
control (3 USA patents), computer vision (1 USA patent), data mining (1 USA
patent), optimization, decision support and elsewhere.
Some
related images.
Evaluating Probability Forecasts
Abstract: Probability forecasts of events are
routinely used in climate predictions, in forecasting default probabilities on
bank loans, or in estimating the probability of a patient's positive response
to treatment. Scoring rules have long been used to assess the efficacy of the
forecast probabilities after observing the occurrence, or non-occurrence, of
the predicted events. We develop a statistical theory for scoring rules and
propose an alternative approach to the evaluation of probability forecasts.
This approach uses loss functions relating the predicted to the actual
probabilities of the events, and applies martingale theory to exploit the
temporal structure between the forecast and the subsequent occurrence or
non-occurrence of the event.
In Epidemiology, a variety of indices, such as PPV (positive predictive value),
NPV, predictiveness curve, the area under the ROC
curve and R2 difference between models are routinely used, without adequate
inferential tools. We provide such tools.
Hidden features of financial markets
Abstract: The ensuing economic crisis has
re-emphasized the need to study and understand the dynamics of the stock
market. Furthermore, the fact that the crisis itself, with its magnitude and
severity, was poorly predicted by existing economic theories highlights the
need to rethink certain economic key concepts. Such attempts are carried out by
Econophysicists, who have been performing rigorous
empirical and analytical research on financial markets for the past two
decades. One of the focuses of these investigations has been the correlations
between stock price movements, and the extraction of meaningful information out
of these correlations regarding the behavior of the market. This talk will
introduce new methods, based on the concept of stock partial correlations, to
uncover important characteristics of financial markets. After an overview of
the relevant concepts, two new methods will be presented - the stock dependency
networks, and the Index Cohesive Force (ICF). These methods have been used to
study the New-York stock market (NYSE) and the Tel-Aviv stock market (TASE).
The result of this study was a successful uncovering of hidden features of
these markets, features that were previously unobservable in the standard stock
correlations. The main findings of this study will be presented, following by a
discussion of the possible applications of these methodologies in economic
practice.
Joint work with Eshel Ben-Jacob
Aggregate Diffusion Dynamics in Agent-Based Models with a Spatial
Structure
Abstract: The diffusion or adoption of new
products (such as fax machines, skype, facebook, Ipad, etc.) is one of
the key problems in Marketing research. In recent years, this problem was often
studied numerically, using agent-based models (ABMs). In this talk I will focus
on analysis of the aggregate diffusion dynamics in ABMs with a spatial
structure. In one-dimensional ABMs, the aggregate diffusion dynamics can be
explicitly calculated, without using the mean-field approximation. In multidimensional
ABMs, we introduce a clusters-dynamics approach, and use it to derive an
analytic approximation of the aggregate diffusion dynamics. The
clusters-dynamics approximation shows that the aggregate diffusion dynamics
does not depend on the average distance between individuals, but rather on the
expansion rate of clusters of adopters. Therefore, the grid dimension has a
large effect on the aggregate adoption dynamics, but a small-world structure
and heterogeneity among individuals have only a minor effect. Our results
suggest that the one-dimensional model and the fully-connected Bass model
provide a lower bound and an upper bound, respectively, for the aggregate
diffusion dynamics in agent-based models with "any" spatial
structure.
This is joint work with Ro'i Gibori
and Eitan Muller
Harmonic Analysis of Transposable Arrays
Abstract: "Transposable Arrays" (TA)
are data matrices in which both rows and columns should be treated as features
and have nontrivial correlation structure. This data type is ubiquitous in
modern applications (e.g. gene microarrays, recommender systems, text-document
matrices), where analysis often aims at common tasks and encounters common
difficulies. Tasks of interest include finding interpretable structure for the
row set and the column set, missing value imputation, quantization, denoising
and anomaly detection. Still, most known treatments of TA data are ad-hoc.
I will describe a nonparametric model allowing
systematic treatment of TA's (and, more generally, higher rank data tensors)
and algorithms for performing these tasks. Our treatment is motivated by a
theorem of J.O.Stromberg, whereby the tensor product of Haar bases is extremely
efficient in describing functions of bounded mixed derivatives in high
dimensions. Fitting the model means simultaneously organizing the rows and
columns of the TA to yield small "mixed variation". Once fitted, the
above tasks are performed in the coefficient domain of the tensor product of
Haar-like bases.
Any interpretable TA analysis produce complicated
output, which is hard to visualize on paper. As a computational interlude,
we'll play with an interactive user interface developed to explore the output
of TA analysis algorithms.
Joint work with Ronald Coifman (Yale) and Boaz Nadler (Weizmann).
References: Haar-like
bases (ICML 2010) ; Harmonic analysis of
data bases (Book chapter)
- Marina Bogomolov, Tel Aviv University
Hierarchical Testing of Subsets of Hypotheses
Abstract: As the size of large testing problems
encountered in practice keeps increasing, more of these problems have further
structure where the set of hypotheses can be partitioned into subsets of the
hypotheses, and a discovery of some signal in a subset is of interest on top of
the discovery of a signal in each of the many hypothesis on its own.
Furthermore, the true state of the tested signals tends to be more similar
within these subsets than across the subsets. Examples are regions in the brain
in functional MRI research, sets of genes in genomic research, or geographical
areas in disease outbreaks monitoring. The challenges in the analysis of such
multiple testing problems will be discussed, and previous efforts to address
them will be reviewed. We then present a few new methods to control various
aspects of the False Discovery Rate, and discuss their benefits and
limitations.
Joint work with Yoav Benjamini. This talk is part of PhD thesis defense.
Functional Time-Series Prediction: Application to the
Prediction of the Daily Power Demand Shapes for the Electricity Authority of
Cyprus
Abstract: We consider the prediction problem of
a time series on a whole time interval in terms of its past.
The approach that we adopt is based on functional kernel non-parametric
regression estimation techniques where observations are discrete recordings of
segments of an underlying stochastic process considered as curves. We estimate
conditional expectations by using appropriate wavelet decompositions of the
segmented sample paths. We also propose a method to select the bandwidth for
functional time series prediction. The idea underlying this method is to
calculate the empirical risk of prediction using past segments of the observed
series and to select as value of the bandwidth for prediction the bandwidth
which minimizes this risk. We illustrate the usefulness of the proposed
functional wavelet-kernel prediction methodology to the prediction of the daily
power demand shapes for the Electricity Authority of Cyprus. Some recent
advances will also be discussed.
(This is joint work with Anestis Antoniadis (Univesrite Joseph Fourier, France) and Efstathios
Paparoditis (University of Cyprus, Cyprus).)
Generalized Alpha Investing: Definitions, Optimality
Results, and Application to Public Databases
Abstract: The increasing prevalence and utility
of large, public databases necessitates the development of appropriate methods
for controlling false discovery. Motivated by this problem, we discuss the
generic problem of testing a possibly infinite stream of null hypotheses. In
this context, Foster and Stine (2007) proposed a false discovery measure they
called mFDR, and an approach for controlling it named
alpha investing. We generalize alpha investing and use our generalization to
derive optimal allocation rules for the case of simple hypotheses. We
demonstrate empirically that this approach is more powerful than alpha
investing while controlling mFDR.
We then present the concept of quality preserving databases (QPD), originally
introduced in Aharoni et al. (2010), which formalizes efficient public database
management to simultaneously save costs and control false discovery. We show
how one variant or generalized alpha investing can be used to control mFDR in a QPD and lead to significant reduction in costs
compared to na¨ıve approaches for controlling
the family-wise error rate implemented in Aharoni et al. (2010).
Joint work with Saharon Rosset of Tel Aviv University.
Strategies for Data Analysis with Two Types of Missing
Values
Abstract: Analysis of incomplete data requires
assumptions about the mechanism that divides the complete sample into its
observed and missing parts. When two different types of missing values occur in
the same data set, one should also consider the process that partitions the
missing data into the two groups. In this presentation, I extend Rubin’s (1976)
concept of missing at random to two sets of missing values, describing
conditions under which the missing-data processes may be completely or
partially ignored. Multiple imputation (Rubin, 1987)
may be carried out in two stages, allowing us to measure rates of missing
information due to each type of missing value. For illustration, I apply these
concepts and techniques to several data examples. (This is joint work with Joe
Schafer).
- Adi Wyner, The Wharton School, University of
Pennsylvania