2014 Workshop on
Statistical Physics of Disordered Systems
and Its Applications (SPDSA2014)
--- Inverse Problems and Statistical Machine Learning Theory ---
Schedule: 10 March, 2014
Scientific Program:
Organized session only: We do not accept submissions from non-invited speakers.
10:20-10:30 Opening
10:30-12:00 Session 1
Keisuke Yamazaki (Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Japan)
Title: Phase Transition in Bayes Statistics
Abstract:
Hierarchical statistical models such as mixture models and graphical models with latent nodes have singularities in the parameter space.
The algebraic geometrical method has been developed for the analysis of the singularities and the asymptotic performance of the models has been elucidated in the Bayes estimation.
According to the method, there is the phase transition in the log marginal likelihood.
The hyperparameter in a prior distribution is the order parameter and plays an important role to determine the performance.
We show the connection between the phases and the estimated structures of the model.
Chiou-Ting Candy Hsu (Department of Computer Science, National Tsing Hua University, Taiwan, R.O.C)
Title: Simultaneous Tensor Decomposition and Completion Using Factor Priors
Abstract
The success of research on matrix completion is evident in a variety of real-world applications. Tensor completion has also generated a great deal of research interest in recent years.
Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors.
In this talk, I will introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure.
I will talk about our proposed method called Simultaneous Tensor Decomposition and Completion (STDC), which combines a rank minimization technique with Tucker model decomposition.
Moreover, we use factor priors to characterize the underlying joint-manifold drawn from the model factors.
By exploiting this auxiliary information, our method leverages two classic schemes and accurately estimates the model factors and missing entries.
Experimental results will also be shown to demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications.
12:00-14:00 Lunch
14:00-15:30 Session 2
Aurelien Decelle (Dipartmento di Fisica, Universitá di Roma, "La Sapienza", Italy)
Title: A Pseudo-Likelihood Decimation Algorithm Improving the Inference of the Interaction Network in a General Class of Ising Models
Abstract:
In the ultimate years, inferring complex systems made of strong interactions between many particles has focused a lot of attention.
Many works have been done in different fields such as physics, social science, computer science or even biology.
The inference aims to retrieve the parameters of a model for which it is believe that the system can be described.
It therefore gives precious information about the nature of the system.
In our recent work, we have developed a new method based on the maximization of the likelihood in order to recover the topology of interactions of complex systems well-described by the Ising model.
In our approach we decimate unnecessary parameters to the description of the model. We apply and test our technique on both the static and dynamic Ising inverse problem and compare it to the classical L1 method.
Muneki Yasuda (Graduate School of Science and Engineering, Yamagata University, Japan)
Title: Composite Likelihood Estimation for Inverse Ising Problem
Abstract:
Maximum composite likelihood estimation (MCLE) is a statistical approximation of the maximum likelihood estimation that is a higher-order generalization of the maximum pseudo likelihood estimation (MPLE).
An asymptotic analysis shows that MCLE is statistically more efficient than MPLE in terms of the asymptotic variance, and shows that MCLE is asymptotically consistent as well as MPLE.
In MPLE, we focus a one-site likelihood function and maximize the average of the one-cite likelihood functions.
On the other hand, we focus a block likelihood function, which consists of likelihood functions of multiple sites in MCLE.
In this talk, I will apply MCLE to the inverse Ising problem and, furthermore, will discuss an expansion of the concept of MCLE to another problem.
15:30-15:45 Break
15:45-17:15 Session 3
Ulisse Ferrari (Laboratoire de Physique Theorique de l'Ecole Normale Superieure, Paris, France)
Title: Inferred Model of the Prefrontal Cortex Activity Unveils Task-Related Cell Assemblies and Memory Replay
Abstract:
Cell assemblies are thought to be the units of information representation in the brain, yet their detection from experimental data is arduous.
Here, we propose to infer the effective network structure from simultaneously recorded neurons in prefrontal cortex using an inverse Ising model.
We define cell assemblies as the co-activated neurons in the dynamics of the resulting abstract neural network.
Different dynamical regimes, as may be observed across wakefulness and sleep, can be reproduced by changing a global input parameter, providing access to rare activity fluctuations, crucial for cell assembly replay.
The identified assemblies strongly co-activate during wakeful experience and are found to replay during subsequent sleep, in correspondence to the potentiation of the inferred network.
Across sessions, a variety of different network scenarios is observed, providing insight in cell assembly formation and replay.
Tomoyuki Obuchi (Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Japan)
Title: Properties of Probability Distributions Constrained by Observables: Implication to Maximum Entropy Modeling
Abstract:
In many cases in inverse problem, the maximum entropy principle (MEP) is employed as a minimum assumption to specify the functional form, which naturally leads the Boltzmann distribution.
Though this assumption is known to work well in many applications, the efficiency or the limitation of the assumption itself remains unclear.
To obtain insights about this point, we formulate inverse problems in a general setting and compute the number of probability distributions satisfying the given constraints.
The results with the completely-random constraints seem to show the MEP provides no benefit for inference.
However, in the more realistic case of structured constraints and target distribution, we expect the MEP becomes useful.
This is currently investigated by numerics and some positive results are actually obtained.
In the talk, we will present these analytical and numerical results with explaining some concepts clarified in our analysis.
17:15-17:30 Closing
Registration Fee: Free
Organizers expect many reserachers and students in the related reserach fields
to attend the present workshop.
Organized by
Masayuki Ohzeki (Graduate School of Informatics, Kyoto University, Japan)
Kazuyuki Tanaka (Graduate School of Information Sciences, Tohoku University, Japan)
Supported by
Grant-in-Aid for Scientific Research on Innovative Areas ``Initiative for High-Demensional Data-Driven Science through Deepening of Sparse Modeling'' (Head Investigator: Masato Okada, University of Tokyo, Japan)
Graduate School of Informatics, Kyoto University, Japan
Graduate School of Information Sciences, Tohoku University, Japan
Related Webpages
Workshop on Statistical Physics of Disordered Systems and Its Applications (SPDSA2013) --- Prologue Series V of FSPIP2013 --- (March, 2013, Sendai, Japan)
Frontier of Statistical Physics and Information Processing --- Perspectives from Nonequilibrium Behaviors --- (FSPIP2013) (July, 2013, Kyoto, Japan)
ELC International Meeting on ''Inference, Computation, and Spin Glasses'' (ICSG2013), (July, 2013, Sapporo, Japan)
Contact to SPDSA2014 office