Spontaneous Clustering via Minimum Gamma-divergence

Open House, ISM in Tachikawa, 2013.6.14統計数理研究所オープンハウス（立川）、H25.6.14ポスター発

Minimization Problems Based on Relative α\alpha-Entropy II: Reverse Projection

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted $\mathscr{I}_{\alpha}$) were studied. Such minimizers were called forward $\mathscr{I}_{\alpha}$-projections. Here, a complementary class of minimization problems leading to the so-called reverse $\mathscr{I}_{\alpha}$-projections are studied. Reverse $\mathscr{I}_{\alpha}$-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems ($\alpha >1$) and in constrained compression settings ($\alpha <1$). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse $\mathscr{I}_{\alpha}$-projection into a forward $\mathscr{I}_{\alpha}$-projection. The transformed problem is a simpler quasiconvex minimization subject to linear constraints.Comment: 20 pages; 3 figures; minor change in the title; revised manuscript. Accepted for publication in IEEE Transactions on Information Theor

Robust Learning from Multiple Information Sources

In the big data era, the ability to handle high-volume, high-velocity and high-variety information assets has become a basic requirement for data analysts. Traditional learning models, which focus on medium size, single source data, often fail to achieve reliable performance if data come from multiple heterogeneous sources (views). As a result, robust multi-view data processing methods that are insensitive to corruptions and anomalies in the data set are needed. This thesis develops robust learning methods for three problems that arise from real-world applications: robust training on a noisy training set, multi-view learning in the presence of between-view inconsistency and network topology inference using partially observed data. The central theme behind all these methods is the use of information-theoretic measures, including entropies and information divergences, as parsimonious representations of uncertainties in the data, as robust optimization surrogates that allows for efficient learning, and as flexible and reliable discrepancy measures for data fusion. More specifically, the thesis makes the following contributions: 1. We propose a maximum entropy-based discriminative learning model that incorporates the minimal entropy (ME) set anomaly detection technique. The resulting probabilistic model can perform both nonparametric classification and anomaly detection simultaneously. An efficient algorithm is then introduced to estimate the posterior distribution of the model parameters while selecting anomalies in the training data. 2. We consider a multi-view classification problem on a statistical manifold where class labels are provided by probabilistic density functions (p.d.f.) and may not be consistent among different views due to the existence of noise corruption. A stochastic consensus-based multi-view learning model is proposed to fuse predictive information for multiple views together. By exploring the non-Euclidean structure of the statistical manifold, a joint consensus view is constructed that is robust to single-view noise corruption and between-view inconsistency. 3. We present a method for estimating the parameters (partial correlations) of a Gaussian graphical model that learns a sparse sub-network topology from partially observed relational data. This model is applicable to the situation where the partial correlations between pairs of variables on a measured sub-network (internal data) are to be estimated when only summary information about the partial correlations between variables outside of the sub-network (external data) are available. The proposed model is able to incorporate the dependence structure between latent variables from external sources and perform latent feature selection efficiently. From a multi-view learning perspective, it can be seen as a two-view learning system given asymmetric information flow from both the internal view and the external view.PHDElectrical & Computer Eng PhDUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138599/1/tianpei_1.pd

Entropy and Divergence Associated with Power Function and the Statistical Application

In statistical physics, Boltzmann-Shannon entropy provides good understanding for the equilibrium states of a number of phenomena. In statistics, the entropy corresponds to the maximum likelihood method, in which Kullback-Leibler divergence connects Boltzmann-Shannon entropy and the expected log-likelihood function. The maximum likelihood estimation has been supported for the optimal performance, which is known to be easily broken down in the presence of a small degree of model uncertainty. To deal with this problem, a new statistical method, closely related to Tsallis entropy, is proposed and shown to be robust for outliers, and we discuss a local learning property associated with the method