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Bin Yu

Publications and source records attributed to Bin Yu.

At least 199 records · Page 11Linked to original sources
arXiv2014

Concise comparative summaries (CCS) of large text corpora with a human experiment

In this paper we propose a general framework for topic-specific summarization of large text corpora and illustrate how it can be used for the analysis of news databases. Our framework, concise comparative summarization (CCS), is built on sparse classification methods. CCS is a lightweight and flexible tool that offers a compromise between simple word frequency based methods currently in wide use and more heavyweight, model-intensive methods such as latent Dirichlet allocation (LDA). We argue that sparse methods have much to offer for text analysis and hope CCS opens the door for a new branch of research in this important field. For a particular topic of interest (e.g., China or energy), CSS automatically labels documents as being either on- or off-topic (usually via keyword search), and then uses sparse classification methods to predict these labels with the high-dimensional counts of all the other words and phrases in the documents. The resulting small set of phrases found as predictive are then harvested as the summary. To validate our tool, we, using news articles from the New York Times international section, designed and conducted a human survey to compare the different summarizers with human understanding. We demonstrate our approach with two case studies, a media analysis of the framing of "Egypt" in the New York Times throughout the Arab Spring and an informal comparison of the New York Times' and Wall Street Journal's coverage of "energy." Overall, we find that the Lasso with $L^2$ normalization can be effectively and usefully used to summarize large corpora, regardless of document size.

cs.CL↗
arXiv2014

Depth $0$ Nonsingular Morse Smale flows on $S^3$

In this paper, we first develope the concept of Lyapunov graph to weighted Lyapunov graph (abbreviated as WLG) for nonsingular Morse-Smale flows (abbreviated as NMS flows) on $S^3$. WLG is quite sensitive to NMS flows on $S^3$. For instance, WLG detect the indexed links of NMS flows. Then we use WLG and some other tools to describe nonsingular Morse-Smale flows without heteroclinic trajectories connecting saddle orbits (abbreviated as depth $0$ NMS flows). It mainly contains the following several directions: \begin{enumerate} \item we use WLG to list depth $0$ NMS flows on $S^3$; \item with the help of WLG, comparing with Wada's algorithm, we provide a direct description about the (indexed) link of depth $0$ NMS flows; \item to overcome the weakness that WLG can't decide topologically equivalent class, we give a simplified Umanskii Theorem to decide when two depth $0$ NMS flows on $S^3$ are topological equivalence; \item under these theories, we classify (up to topological equivalence) all depth 0 NMS flows on $S^3$ with periodic orbits number no more than 4. \end{enumerate}

math.DS↗
arXiv2014

Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs

Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great interest to describe and understand the space of such classes. However, with currently known algorithms, sampling over such classes is only feasible for graphs with fewer than approximately 20 vertices. In this paper, we design reversible irreducible Markov chains on the space of Markov equivalent classes by proposing a perfect set of operators that determine the transitions of the Markov chain. The stationary distribution of a proposed Markov chain has a closed form and can be computed easily. Specifically, we construct a concrete perfect set of operators on sparse Markov equivalence classes by introducing appropriate conditions on each possible operator. Algorithms and their accelerated versions are provided to efficiently generate Markov chains and to explore properties of Markov equivalence classes of sparse directed acyclic graphs (DAGs) with thousands of vertices. We find experimentally that in most Markov equivalence classes of sparse DAGs, (1) most edges are directed, (2) most undirected subgraphs are small and (3) the number of these undirected subgraphs grows approximately linearly with the number of vertices. The article contains supplement arXiv:1303.0632, http://dx.doi.org/10.1214/13-AOS1125SUPP

stat.ML↗
arXiv2014

The shuffle estimator for explainable variance in fMRI experiments

In computational neuroscience, it is important to estimate well the proportion of signal variance in the total variance of neural activity measurements. This explainable variance measure helps neuroscientists assess the adequacy of predictive models that describe how images are encoded in the brain. Complicating the estimation problem are strong noise correlations, which may confound the neural responses corresponding to the stimuli. If not properly taken into account, the correlations could inflate the explainable variance estimates and suggest false possible prediction accuracies. We propose a novel method to estimate the explainable variance in functional MRI (fMRI) brain activity measurements when there are strong correlations in the noise. Our shuffle estimator is nonparametric, unbiased, and built upon the random effect model reflecting the randomization in the fMRI data collection process. Leveraging symmetries in the measurements, our estimator is obtained by appropriately permuting the measurement vector in such a way that the noise covariance structure is intact but the explainable variance is changed after the permutation. This difference is then used to estimate the explainable variance. We validate the properties of the proposed method in simulation experiments. For the image-fMRI data, we show that the shuffle estimates can explain the variation in prediction accuracy for voxels within the primary visual cortex (V1) better than alternative parametric methods.

stat.AP↗
arXiv2014

Asymptotic Properties of Lasso+mLS and Lasso+Ridge in Sparse High-dimensional Linear Regression

We study the asymptotic properties of Lasso+mLS and Lasso+Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we propose a valid inference procedure for parameter estimation based on parametric residual bootstrap after Lasso+mLS and Lasso+Ridge. Second, we derive the asymptotic unbiasedness of Lasso+mLS and Lasso+Ridge. More specifically, we show that their biases decay at an exponential rate and they can achieve the oracle convergence rate of $s/n$ (where $s$ is the number of nonzero regression coefficients and $n$ is the sample size) for mean squared error (MSE). Third, we show that Lasso+mLS and Lasso+Ridge are asymptotically normal. They have an oracle property in the sense that they can select the true predictors with probability converging to 1 and the estimates of nonzero parameters have the same asymptotic normal distribution that they would have if the zero parameters were known in advance. In fact, our analysis is not limited to adopting Lasso in the selection stage, but is applicable to any other model selection criteria with exponentially decay rates of the probability of selecting wrong models.

math.ST↗
arXiv2013

Stability

Reproducibility is imperative for any scientific discovery. More often than not, modern scientific findings rely on statistical analysis of high-dimensional data. At a minimum, reproducibility manifests itself in stability of statistical results relative to "reasonable" perturbations to data and to the model used. Jacknife, bootstrap, and cross-validation are based on perturbations to data, while robust statistics methods deal with perturbations to models. In this article, a case is made for the importance of stability in statistics. Firstly, we motivate the necessity of stability for interpretable and reliable encoding models from brain fMRI signals. Secondly, we find strong evidence in the literature to demonstrate the central role of stability in statistical inference, such as sensitivity analysis and effect detection. Thirdly, a smoothing parameter selector based on estimation stability (ES), ES-CV, is proposed for Lasso, in order to bring stability to bear on cross-validation (CV). ES-CV is then utilized in the encoding models to reduce the number of predictors by 60% with almost no loss (1.3%) of prediction performance across over 2,000 voxels. Last, a novel "stability" argument is seen to drive new results that shed light on the intriguing interactions between sample to sample variability and heavier tail error distribution (e.g., double-exponential) in high-dimensional regression models with $p$ predictors and $n$ independent samples. In particular, when $p/n\rightarrowκ\in(0.3,1)$ and the error distribution is double-exponential, the Ordinary Least Squares (OLS) is a better estimator than the Least Absolute Deviation (LAD) estimator.

math.ST↗
arXiv2013

Supervised Feature Selection in Graphs with Path Coding Penalties and Network Flows

We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to automatically select a subgraph with few connected components; by exploiting prior knowledge, one can indeed improve the prediction performance or obtain results that are easier to interpret. Regularization or penalty functions for selecting features in graphs have recently been proposed, but they raise new algorithmic challenges. For example, they typically require solving a combinatorially hard selection problem among all connected subgraphs. In this paper, we propose computationally feasible strategies to select a sparse and well-connected subset of features sitting on a directed acyclic graph (DAG). We introduce structured sparsity penalties over paths on a DAG called "path coding" penalties. Unlike existing regularization functions that model long-range interactions between features in a graph, path coding penalties are tractable. The penalties and their proximal operators involve path selection problems, which we efficiently solve by leveraging network flow optimization. We experimentally show on synthetic, image, and genomic data that our approach is scalable and leads to more connected subgraphs than other regularization functions for graphs.

stat.ML↗
arXiv2013

Error Rate Bounds in Crowdsourcing Models

Crowdsourcing is an effective tool for human-powered computation on many tasks challenging for computers. In this paper, we provide finite-sample exponential bounds on the error rate (in probability and in expectation) of hyperplane binary labeling rules under the Dawid-Skene crowdsourcing model. The bounds can be applied to analyze many common prediction methods, including the majority voting and weighted majority voting. These bound results could be useful for controlling the error rate and designing better algorithms. We show that the oracle Maximum A Posterior (MAP) rule approximately optimizes our upper bound on the mean error rate for any hyperplane binary labeling rule, and propose a simple data-driven weighted majority voting (WMV) rule (called one-step WMV) that attempts to approximate the oracle MAP and has a provable theoretical guarantee on the error rate. Moreover, we use simulated and real data to demonstrate that the data-driven EM-MAP rule is a good approximation to the oracle MAP rule, and to demonstrate that the mean error rate of the data-driven EM-MAP rule is also bounded by the mean error rate bound of the oracle MAP rule with estimated parameters plugging into the bound.

stat.ML↗
arXiv2013

A Statistical Perspective on Algorithmic Leveraging

One popular method for dealing with large-scale data sets is sampling. For example, by using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales rows/columns of data matrices to reduce the data size before performing computations on the subproblem. This method has been successful in improving computational efficiency of algorithms for matrix problems such as least-squares approximation, least absolute deviations approximation, and low-rank matrix approximation. Existing work has focused on algorithmic issues such as worst-case running times and numerical issues associated with providing high-quality implementations, but none of it addresses statistical aspects of this method. In this paper, we provide a simple yet effective framework to evaluate the statistical properties of algorithmic leveraging in the context of estimating parameters in a linear regression model with a fixed number of predictors. We show that from the statistical perspective of bias and variance, neither leverage-based sampling nor uniform sampling dominates the other. This result is particularly striking, given the well-known result that, from the algorithmic perspective of worst-case analysis, leverage-based sampling provides uniformly superior worst-case algorithmic results, when compared with uniform sampling. Based on these theoretical results, we propose and analyze two new leveraging algorithms. A detailed empirical evaluation of existing leverage-based methods as well as these two new methods is carried out on both synthetic and real data sets. The empirical results indicate that our theory is a good predictor of practical performance of existing and new leverage-based algorithms and that the new algorithms achieve improved performance.

stat.ME↗
arXiv2013

Early stopping and non-parametric regression: An optimal data-dependent stopping rule

The strategy of early stopping is a regularization technique based on choosing a stopping time for an iterative algorithm. Focusing on non-parametric regression in a reproducing kernel Hilbert space, we analyze the early stopping strategy for a form of gradient-descent applied to the least-squares loss function. We propose a data-dependent stopping rule that does not involve hold-out or cross-validation data, and we prove upper bounds on the squared error of the resulting function estimate, measured in either the $L^2(P)$ and $L^2(P_n)$ norm. These upper bounds lead to minimax-optimal rates for various kernel classes, including Sobolev smoothness classes and other forms of reproducing kernel Hilbert spaces. We show through simulation that our stopping rule compares favorably to two other stopping rules, one based on hold-out data and the other based on Stein's unbiased risk estimate. We also establish a tight connection between our early stopping strategy and the solution path of a kernel ridge regression estimator.

stat.ML↗
arXiv2013

Geometry of the faithfulness assumption in causal inference

Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces in a hypercube. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and strong-faithfulness has been proposed and assumed to achieve uniform or high-dimensional consistency. In contrast to the plain faithfulness assumption, the set of distributions that is not strong-faithful has nonzero Lebesgue measure and in fact, can be surprisingly large as we show in this paper. We study the strong-faithfulness condition from a geometric and combinatorial point of view and give upper and lower bounds on the Lebesgue measure of strong-faithful distributions for various classes of directed acyclic graphs. Our results imply fundamental limitations for the PC-algorithm and potentially also for other algorithms based on partial correlation testing in the Gaussian case.

math.ST↗
arXiv2013

A Unified Framework for High-Dimensional Analysis of M-Estimators with Decomposable Regularizers

High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a line of recent work has studied models with various types of low-dimensional structure, including sparse vectors, sparse and structured matrices, low-rank matrices and combinations thereof. In such settings, a general approach to estimation is to solve a regularized optimization problem, which combines a loss function measuring how well the model fits the data with some regularization function that encourages the assumed structure. This paper provides a unified framework for establishing consistency and convergence rates for such regularized M-estimators under high-dimensional scaling. We state one main theorem and show how it can be used to re-derive some existing results, and also to obtain a number of new results on consistency and convergence rates, in both $\ell_2$-error and related norms. Our analysis also identifies two key properties of loss and regularization functions, referred to as restricted strong convexity and decomposability, that ensure corresponding regularized M-estimators have fast convergence rates and which are optimal in many well-studied cases.

math.ST↗
arXiv2013

Scaling Analysis of Nanowire Phase Change Memory

This letter analyzes the scaling property of nanowire (NW) phase change memory (PCM) using analytic and numerical methods. The scaling scenarios of the three widely-used NW PCM peration schemes (constant electric field, voltage, and current) are studied and compared. It is shown that if the device size is downscaled by a factor of 1/k (k>1), the peration energy (current) will be reduced by more than k3 (k) times, and the operation speed will be increased by k2 times. It is also shown that more than 90% of operation energy is wasted as thermal flux into substrate and electrodes. We predict that, if the wasted thermal flux is effectively reduced by heat confinement technologies, the energy consumed per RESET operation can be decreased from about 1 pJ to less than 100 fJ. It is shown that reducing NW aspect ratio (AR) helps decreasing PCM energy consumption. It is revealed that cross-cell thermal proximity disturbance is counter-intuitively alleviated by scaling, leading to a desirable scaling scenario.

cond-mat.mes-hall↗
arXiv2012

A Hierarchical Bayesian Approach for Aerosol Retrieval Using MISR Data

Atmospheric aerosols can cause serious damage to human health and life expectancy. Using the radiances observed by NASA's Multi-angle Imaging SpectroRadiometer (MISR), the current MISR operational algorithm retrieves Aerosol Optical Depth (AOD) at a spatial resolution of 17.6 km x 17.6 km. A systematic study of aerosols and their impact on public health, especially in highly-populated urban areas, requires a finer-resolution estimate of the spatial distribution of AOD values. We embed MISR's operational weighted least squares criterion and its forward simulations for AOD retrieval in a likelihood framework and further expand it into a Bayesian hierarchical model to adapt to a finer spatial scale of 4.4 km x 4.4 km. To take advantage of AOD's spatial smoothness, our method borrows strength from data at neighboring pixels by postulating a Gaussian Markov Random Field prior for AOD. Our model considers both AOD and aerosol mixing vectors as continuous variables. The inference of AOD and mixing vectors is carried out using Metropolis-within-Gibbs sampling methods. Retrieval uncertainties are quantified by posterior variabilities. We also implement a parallel MCMC algorithm to reduce computational cost. We assess our retrievals performance using ground-based measurements from the AErosol RObotic NETwork (AERONET), a hand-held sunphotometer and satellite images from Google Earth. Based on case studies in the greater Beijing area, China, we show that a 4.4 km resolution can improve the accuracy and coverage of remotely-sensed aerosol retrievals, as well as our understanding of the spatial and seasonal behaviors of aerosols. This improvement is particularly important during high-AOD events, which often indicate severe air pollution.

stat.AP↗
arXiv2012

Complexity Analysis of the Lasso Regularization Path

The regularization path of the Lasso can be shown to be piecewise linear, making it possible to "follow" and explicitly compute the entire path. We analyze in this paper this popular strategy, and prove that its worst case complexity is exponential in the number of variables. We then oppose this pessimistic result to an (optimistic) approximate analysis: We show that an approximate path with at most O(1/sqrt(epsilon)) linear segments can always be obtained, where every point on the path is guaranteed to be optimal up to a relative epsilon-duality gap. We complete our theoretical analysis with a practical algorithm to compute these approximate paths.

stat.ML↗
arXiv2011

Minimax-optimal rates for sparse additive models over kernel classes via convex programming

Sparse additive models are families of $d$-variate functions that have the additive decomposition $f^* = \sum_{j \in S} f^*_j$, where $S$ is an unknown subset of cardinality $s \ll d$. In this paper, we consider the case where each univariate component function $f^*_j$ lies in a reproducing kernel Hilbert space (RKHS), and analyze a method for estimating the unknown function $f^*$ based on kernels combined with $\ell_1$-type convex regularization. Working within a high-dimensional framework that allows both the dimension $d$ and sparsity $s$ to increase with $n$, we derive convergence rates (upper bounds) in the $L^2(\mathbb{P})$ and $L^2(\mathbb{P}_n)$ norms over the class $\MyBigClass$ of sparse additive models with each univariate function $f^*_j$ in the unit ball of a univariate RKHS with bounded kernel function. We complement our upper bounds by deriving minimax lower bounds on the $L^2(\mathbb{P})$ error, thereby showing the optimality of our method. Thus, we obtain optimal minimax rates for many interesting classes of sparse additive models, including polynomials, splines, and Sobolev classes. We also show that if, in contrast to our univariate conditions, the multivariate function class is assumed to be globally bounded, then much faster estimation rates are possible for any sparsity $s = Ω(\sqrt{n})$, showing that global boundedness is a significant restriction in the high-dimensional setting.

math.ST↗
arXiv2011

Spectral clustering and the high-dimensional stochastic blockmodel

Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of highly connected actors form an essential feature in the structure of several empirical networks. Spectral clustering is a popular and computationally feasible method to discover these communities. The stochastic blockmodel [Social Networks 5 (1983) 109--137] is a social network model with well-defined communities; each node is a member of one community. For a network generated from the Stochastic Blockmodel, we bound the number of nodes "misclustered" by spectral clustering. The asymptotic results in this paper are the first clustering results that allow the number of clusters in the model to grow with the number of nodes, hence the name high-dimensional. In order to study spectral clustering under the stochastic blockmodel, we first show that under the more general latent space model, the eigenvectors of the normalized graph Laplacian asymptotically converge to the eigenvectors of a "population" normalized graph Laplacian. Aside from the implication for spectral clustering, this provides insight into a graph visualization technique. Our method of studying the eigenvectors of random matrices is original.

stat.ML↗