Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models

A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include $K$-fold cross-validation ($K$-CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Though these methods work well for low-dimensional problems, they are not suitable in high dimensional settings. In this paper, we present StARS: a new stability-based method for choosing the regularization parameter in high dimensional inference for undirected graphs. The method has a clear interpretation: we use the least amount of regularization that simultaneously makes a graph sparse and replicable under random sampling. This interpretation requires essentially no conditions. Under mild conditions, we show that StARS is partially sparsistent in terms of graph estimation: i.e. with high probability, all the true edges will be included in the selected model even when the graph size diverges with the sample size. Empirically, the performance of StARS is compared with the state-of-the-art model selection procedures, including $K$-CV, AIC, and BIC, on both synthetic data and a real microarray dataset. StARS outperforms all these competing procedures

High Dimensional Semiparametric Gaussian Copula Graphical Models

In this paper, we propose a semiparametric approach, named nonparanormal skeptic, for efficiently and robustly estimating high dimensional undirected graphical models. To achieve modeling flexibility, we consider Gaussian Copula graphical models (or the nonparanormal) as proposed by Liu et al. (2009). To achieve estimation robustness, we exploit nonparametric rank-based correlation coefficient estimators, including Spearman's rho and Kendall's tau. In high dimensional settings, we prove that the nonparanormal skeptic achieves the optimal parametric rate of convergence in both graph and parameter estimation. This celebrating result suggests that the Gaussian copula graphical models can be used as a safe replacement of the popular Gaussian graphical models, even when the data are truly Gaussian. Besides theoretical analysis, we also conduct thorough numerical simulations to compare different estimators for their graph recovery performance under both ideal and noisy settings. The proposed methods are then applied on a large-scale genomic dataset to illustrate their empirical usefulness. The R language software package huge implementing the proposed methods is available on the Comprehensive R Archive Network: http://cran. r-project.org/.Comment: 34 pages, 10 figures; the Annals of Statistics, 201

Sparse Additive Models

We present a new class of methods for high-dimensional nonparametric regression and classification called sparse additive models (SpAM). Our methods combine ideas from sparse linear modeling and additive nonparametric regression. We derive an algorithm for fitting the models that is practical and effective even when the number of covariates is larger than the sample size. SpAM is closely related to the COSSO model of Lin and Zhang (2006), but decouples smoothing and sparsity, enabling the use of arbitrary nonparametric smoothers. An analysis of the theoretical properties of SpAM is given. We also study a greedy estimator that is a nonparametric version of forward stepwise regression. Empirical results on synthetic and real data are presented, showing that SpAM can be effective in fitting sparse nonparametric models in high dimensional data

Learning Fashion Compatibility with Bidirectional LSTMs

The ubiquity of online fashion shopping demands effective recommendation services for customers. In this paper, we study two types of fashion recommendation: (i) suggesting an item that matches existing components in a set to form a stylish outfit (a collection of fashion items), and (ii) generating an outfit with multimodal (images/text) specifications from a user. To this end, we propose to jointly learn a visual-semantic embedding and the compatibility relationships among fashion items in an end-to-end fashion. More specifically, we consider a fashion outfit to be a sequence (usually from top to bottom and then accessories) and each item in the outfit as a time step. Given the fashion items in an outfit, we train a bidirectional LSTM (Bi-LSTM) model to sequentially predict the next item conditioned on previous ones to learn their compatibility relationships. Further, we learn a visual-semantic space by regressing image features to their semantic representations aiming to inject attribute and category information as a regularization for training the LSTM. The trained network can not only perform the aforementioned recommendations effectively but also predict the compatibility of a given outfit. We conduct extensive experiments on our newly collected Polyvore dataset, and the results provide strong qualitative and quantitative evidence that our framework outperforms alternative methods.Comment: ACM MM 1

VITON: An Image-based Virtual Try-on Network

We present an image-based VIirtual Try-On Network (VITON) without using 3D information in any form, which seamlessly transfers a desired clothing item onto the corresponding region of a person using a coarse-to-fine strategy. Conditioned upon a new clothing-agnostic yet descriptive person representation, our framework first generates a coarse synthesized image with the target clothing item overlaid on that same person in the same pose. We further enhance the initial blurry clothing area with a refinement network. The network is trained to learn how much detail to utilize from the target clothing item, and where to apply to the person in order to synthesize a photo-realistic image in which the target item deforms naturally with clear visual patterns. Experiments on our newly collected Zalando dataset demonstrate its promise in the image-based virtual try-on task over state-of-the-art generative models

Using Expert Knowledge in Database-Oriented Problem Solving

Database-oriented problem solving often involves the processing of deduction rules which may be recursive in relational database systems. In this kind of problem solving, expert knowledge plays an important role in the guidance of correct and efficient processing. This paper presents a modularized relational planner RELPLAN, which develops a knowledge directed inference and planning mechanism for efficient processing of deduction rules in relational DB systems

Direct solar-pumped iodine laser amplifier

A XeCl laser which was developed earlier for an iodine laser oscillator was modified in order to increase the output pulse energy of XeCl laser so that the iodine laser output energy could be increased. The electrical circuit of the XeCl laser was changed from a simple capacitor discharge circuit of the XeCl laser to a Marx system. Because of this improvement the output energy from the XeCl laser was increased from 60 mj to 80 mj. Subsequently, iodine laser output energy was increased from 100 mj to 3 mj. On the other hand, the energy storage capability and amplification characteristics of the Vortek solar simulator-pumped amplifier was calculated expecting the calculated amplification factor is about 2 and the energy extraction efficiency is 26 percent due to the very low input energy density to the amplifier. As a result of an improved kinetic modeling for the iodine solar simulator pumped power amplifier, it is found that the I-2 along the axis of the tube affects seriously the gain profile. For the gas i-C3F7I at the higher pressures, the gain will decrease due to the I-2 as the pumping intensity increases, and at these higher pressures an increase in flow velocity will increase the gain

Forest Density Estimation

We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to a forest; rather, we form kernel density estimates of the bivariate and univariate marginals, and apply Kruskal's algorithm to estimate the optimal forest on held out data. We prove an oracle inequality on the excess risk of the resulting estimator relative to the risk of the best forest. For graph estimation, we consider the problem of estimating forests with restricted tree sizes. We prove that finding a maximum weight spanning forest with restricted tree size is NP-hard, and develop an approximation algorithm for this problem. Viewing the tree size as a complexity parameter, we then select a forest using data splitting, and prove bounds on excess risk and structure selection consistency of the procedure. Experiments with simulated data and microarray data indicate that the methods are a practical alternative to Gaussian graphical models.Comment: Extended version of earlier paper titled "Tree density estimation