arXiv subjects

Jun Sese

Publications and source records attributed to Jun Sese.

4 recordsLinked to original sources

arXiv2017

Robust sparse Gaussian graphical modeling

Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a high-dimensional graphical model. However, the penalized maximum likelihood procedure is sensitive to outliers. To overcome this problem, we introduce a robust estimation procedure based on the $γ$-divergence. The proposed method has a redescending property, which is known as a desirable property in robust statistics. The parameter estimation procedure is constructed using the Majorize-Minimization algorithm, which guarantees that the objective function monotonically decreases at each iteration. Extensive simulation studies showed that our procedure performed much better than the existing methods, in particular, when the contamination ratio was large. Two real data analyses were carried out to illustrate the usefulness of our proposed procedure.

stat.ME↗

arXiv2016

Support Consistency of Direct Sparse-Change Learning in Markov Networks

We study the problem of learning sparse structure changes between two Markov networks $P$ and $Q$. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes \emph{directly} via estimating the ratio between two Markov network models. In this paper, we give sufficient conditions for \emph{successful change detection} with respect to the sample size $n_p, n_q$, the dimension of data $m$, and the number of changed edges $d$. When using an unbounded density ratio model we prove that the true sparse changes can be consistently identified for $n_p = Ω(d^2 \log \frac{m^2+m}{2})$ and $n_q = Ω({n_p^2})$, with an exponentially decaying upper-bound on learning error. Such sample complexity can be improved to $\min(n_p, n_q) = Ω(d^2 \log \frac{m^2+m}{2})$ when the boundedness of the density ratio model is assumed. Our theoretical guarantee can be applied to a wide range of discrete/continuous Markov networks.

stat.ML↗

arXiv2016

Stochastic Dykstra Algorithms for Metric Learning on Positive Semi-Definite Cone

Recently, covariance descriptors have received much attention as powerful representations of set of points. In this research, we present a new metric learning algorithm for covariance descriptors based on the Dykstra algorithm, in which the current solution is projected onto a half-space at each iteration, and runs at O(n^3) time. We empirically demonstrate that randomizing the order of half-spaces in our Dykstra-based algorithm significantly accelerates the convergence to the optimal solution. Furthermore, we show that our approach yields promising experimental results on pattern recognition tasks.

cs.CV↗

arXiv2011

Least-Squares Independence Regression for Non-Linear Causal Inference under Non-Gaussian Noise

The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called least-squares independence regression (LSIR). LSIR learns the additive noise model through the minimization of an estimator of the squared-loss mutual information between inputs and residuals. A notable advantage of LSIR over existing approaches is that tuning parameters such as the kernel width and the regularization parameter can be naturally optimized by cross-validation, allowing us to avoid overfitting in a data-dependent fashion. Through experiments with real-world datasets, we show that LSIR compares favorably with a state-of-the-art causal inference method.

stat.ML↗