Ying Nian Wu

Dynamic Textures

Dynamic textures are sequences of images of moving scenes that exhibit certain stationarity properties in time; these include sea-waves, smoke, foliage, whirlwind etc. We present a characterization of dynamic textures that poses the problems of modeling, learning, recognizing and synthesizing dynamic textures on a firm analytical footing. We borrow tools from system identification to capture the “essence” of dynamic textures; we do so by learning (i.e. identifying) models that are optimal in the sense of maximum likelihood or minimum prediction error variance. For the special case of second-order stationary processes, we identify the model sub-optimally in closed-form. Once learned, a model has predictive power and can be used for extrapolating synthetic sequences to infinite length with negligible computational cost. We present experimental evidence that, within our framework, even low-dimensional models can capture very complex visual phenomena.

A high-resolution map of active promoters in the human genome

In eukaryotic cells, transcription of every protein-coding gene begins with the assembly of an RNA polymerase II preinitiation complex (PIC) on the promoter. The promoters, in conjunction with enhancers, silencers and insulators, define the combinatorial codes that specify gene expression patterns. Our ability to analyse the control logic encoded in the human genome is currently limited by a lack of accurate information regarding the promoters for most genes. Here we describe a genome-wide map of active promoters in human fibroblast cells, determined by experimentally locating the sites of PIC binding throughout the human genome. This map defines 10,567 active promoters corresponding to 6,763 known genes and at least 1,196 un-annotated transcriptional units. Features of the map suggest extensive use of multiple promoters by the human genes and widespread clustering of active promoters in the genome. In addition, examination of the genome-wide expression profile reveals four general classes of promoters that define the transcriptome of the cell. These results provide a global view of the functional relationships among transcriptional machinery, chromatin structure and gene expression in human cells.

Filters, Random Fields and Maximum Entropy (FRAME): Towards a Unified Theory for Texture Modeling

This article presents a statistical theory for texture modeling. This theory combines filtering theory and Markov random field modeling through the maximum entropy principle, and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view. Our theory characterizes the ensemble of images I with the same texture appearance by a probability distribution f(I) on a random field, and the objective of texture modeling is to make inference about f(I), given a set of observed texture examples.In our theory, texture modeling consists of two steps. (1) A set of filters is selected from a general filter bank to capture features of the texture, these filters are applied to observed texture images, and the histograms of the filtered images are extracted. These histograms are estimates of the marginal distributions of f( I). This step is called feature extraction. (2) The maximum entropy principle is employed to derive a distribution p(I), which is restricted to have the same marginal distributions as those in (1). This p(I) is considered as an estimate of f( I). This step is called feature fusion. A stepwise algorithm is proposed to choose filters from a general filter bank. The resulting model, called FRAME (Filters, Random fields And Maximum Entropy), is a Markov random field (MRF) model, but with a much enriched vocabulary and hence much stronger descriptive ability than the previous MRF models used for texture modeling. Gibbs sampler is adopted to synthesize texture images by drawing typical samples from p(I), thus the model is verified by seeing whether the synthesized texture images have similar visual appearances to the texture images being modeled. Experiments on a variety of 1D and 2D textures are described to illustrate our theory and to show the performance of our algorithms. These experiments demonstrate that many textures which are previously considered as from different categories can be modeled and synthesized in a common framework.

Minimax Entropy Principle and Its Application to Texture Modeling

This article proposes a general theory and methodology, called the minimax entropy principle, for building statistical models for images (or signals) in a variety of applications. This principle consists of two parts. The first is the maximum entropy principle for feature binding (or fusion): for a given set of observed feature statistics, a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them. The second part is the minimum entropy principle for feature selection: among all plausible sets of feature statistics, we choose the set whose maximum entropy distribution has the minimum entropy. Computational and inferential issues in both parts are addressed; in particular, a feature pursuit procedure is proposed for approximately selecting the optimal set of features. The minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics, and an information criterion for feature pursuit is derived. The minimax entropy principle is applied to texture modeling, where a novel Markov random field (MRF) model, called FRAME (filter, random field, and minimax entropy), is derived, and encouraging results are obtained in experiments on a variety of texture images. The relationship between our theory and the mechanisms of neural computation is also discussed.

Dynamic texture recognition

Dynamic textures are sequences of images that exhibit some form of temporal stationarity, such as waves, steam, and foliage. We pose the problem of recognizing and classifying dynamic textures in the space of dynamical systems where each dynamic texture is uniquely represented. Since the space is non-linear, a distance between models must be defined We examine three different distances in the space of autoregressive models and assess their power.

Parameter expansion for data augmentation

Abstract Viewing the observed data of a statistical model as incomplete and augmenting its missing parts are useful for clarifying concepts and central to the invention of two well-known statistical algorithms: expectation-maximization (EM) and data augmentation. Recently, Liu, Rubin, and Wu demonstrated that expanding the parameter space along with augmenting the missing data is useful for accelerating iterative computation in an EM algorithm. The main purpose of this article is to rigorously define a parameter expanded data augmentation (PX-DA) algorithm and to study its theoretical properties. The PX-DA is a special way of using auxiliary variables to accelerate Gibbs sampling algorithms and is closely related to reparameterization techniques. We obtain theoretical results concerning the convergence rate of the PX-DA algorithm and the choice of prior for the expansion parameter. To understand the role of the expansion parameter, we establish a new theory for iterative conditional sampling under the tra...

Efficient Algorithms for Robust Estimation in Linear Mixed-Effects Models Using the Multivariate t Distribution

Linear mixed-effects models are frequently used to analyze repeated measures data, because they model flexibly the within-subject correlation often present in this type of data. The most popular linear mixed-effects model for a continuous response assumes normal distributions for the random effects and the within-subject errors, making it sensitive to outliers. Such outliers are more problematic for mixed-effects models than for fixed-effects models, because they may occur in the random effects, in the within-subject errors, or in both, making them harder to be detected in practice. Motivated by a real dataset from an orthodontic study, we propose a robust hierarchical linear mixed-effects model in which the random effects and the within-subject errors have multivariate t-distributions, with known or unknown degrees-of-freedom, which are allowed to vary with groups of subjects. By using a gamma-normal hierarchical structure, our model allows the identification and classification of both types of outliers, comparing favorably to other multivariate t models for robust estimation in mixed-effects models previously described in the literature, which use only the marginal distribution of the responses. Allowing for unknown degrees-of-freedom, which are estimated from the data, our model provides a balance between robustness and efficiency, leading to reliable results for valid inference. We describe and compare efficient EM-type algorithms, including ECM, ECME, and PX-EM, for maximum likelihood estimation in the robust multivariate t model. We compare the performance of the Gaussian and the multivariatet models under different patterns of outliers. Simulation results indicate that the multivariate t substantially outperforms the Gaussian model when outliers are present in the data, even in moderate amounts.

rMATS: Robust and flexible detection of differential alternative splicing from replicate RNA-Seq data

Significance Alternative splicing (AS) is an important mechanism of eukaryotic gene regulation. Deep RNA sequencing (RNA-Seq) has become a powerful approach for quantitative profiling of AS. With the increasing capacity of high-throughput sequencers, it has become common for RNA-Seq studies of AS to examine multiple biological replicates. We developed rMATS, a new statistical method for robust and flexible detection of differential AS from replicate RNA-Seq data. Besides the analysis of unpaired replicates, rMATS includes a model specifically designed for paired replicates, such as case–control matched pairs in clinical RNA-Seq datasets. We expect rMATS will be useful for genome-wide studies of AS in diverse research projects. Our data also provide new insights about the experimental design for RNA-Seq studies of AS. Ultra-deep RNA sequencing (RNA-Seq) has become a powerful approach for genome-wide analysis of pre-mRNA alternative splicing. We previously developed multivariate analysis of transcript splicing (MATS), a statistical method for detecting differential alternative splicing between two RNA-Seq samples. Here we describe a new statistical model and computer program, replicate MATS (rMATS), designed for detection of differential alternative splicing from replicate RNA-Seq data. rMATS uses a hierarchical model to simultaneously account for sampling uncertainty in individual replicates and variability among replicates. In addition to the analysis of unpaired replicates, rMATS also includes a model specifically designed for paired replicates between sample groups. The hypothesis-testing framework of rMATS is flexible and can assess the statistical significance over any user-defined magnitude of splicing change. The performance of rMATS is evaluated by the analysis of simulated and real RNA-Seq data. rMATS outperformed two existing methods for replicate RNA-Seq data in all simulation settings, and RT-PCR yielded a high validation rate (94%) in an RNA-Seq dataset of prostate cancer cell lines. Our data also provide guiding principles for designing RNA-Seq studies of alternative splicing. We demonstrate that it is essential to incorporate biological replicates in the study design. Of note, pooling RNAs or merging RNA-Seq data from multiple replicates is not an effective approach to account for variability, and the result is particularly sensitive to outliers. The rMATS source code is freely available at rnaseq-mats.sourceforge.net/. As the popularity of RNA-Seq continues to grow, we expect rMATS will be useful for studies of alternative splicing in diverse RNA-Seq projects.

Learning Active Basis Model for Object Detection and Recognition

This article proposes an active basis model, a shared sketch algorithm, and a computational architecture of sum-max maps for representing, learning, and recognizing deformable templates. In our generative model, a deformable template is in the form of an active basis, which consists of a small number of Gabor wavelet elements at selected locations and orientations. These elements are allowed to slightly perturb their locations and orientations before they are linearly combined to generate the observed image. The active basis model, in particular, the locations and the orientations of the basis elements, can be learned from training images by the shared sketch algorithm. The algorithm selects the elements of the active basis sequentially from a dictionary of Gabor wavelets. When an element is selected at each step, the element is shared by all the training images, and the element is perturbed to encode or sketch a nearby edge segment in each training image. The recognition of the deformable template from an image can be accomplished by a computational architecture that alternates the sum maps and the max maps. The computation of the max maps deforms the active basis to match the image data, and the computation of the sum maps scores the template matching by the log-likelihood of the deformed active basis.

Exploring texture ensembles by efficient Markov chain Monte Carlo-Toward a "trichromacy" theory of texture

I E E E Trans on P A M ! , (accepted), 1999. Exploring Texture Ensembles by Efficient Markov Chain Monte Carlo - T o w a r d s a T r i e h r o m a e y T h e o r y of Texture Song C h u n Z h u , X i u Wen Liu, Ying Nian W u Abstract T h i s article presents a m a t h e m a t i c a l definition of texture - the Julesz ensemble 0(h), w h i c h is the set of a l l images (defined on Z ) that share identical statistics h. T h e n texture m o d e l i n g is posed as a n inverse problem: given a set of images sampled from a n u n k n o w n Julesz ensemble fi(h*), we search for the statistics h* w h i c h define the ensemble. A Julesz ensemble fi(h) has a n associated p r o b a b i l i t y d i s t r i b u t i o n g(I;h), w h i c h is uniform over the images i n the ensemble a n d has zero p r o b a b i l i t y outside. I n a c o m p a n i o n paper[32], q(I; h) is shown to be the limit distribution of the F R A M E ( F i l t e r , R a n d o m F i e l d , A n d M i n i m a x E n t r o p y ) model[35] as the image lattice A -~ 7r. T h i s conclusion establishes the intrinsic link between the scientific definition of texture o n Z models of texture o n finite lattices. a n d the m a t h e m a t i c a l It brings two advantages to computer vision. T h e engineering practice of synthesizing texture images by m a t c h i n g statistics has been put o n a m a t h e m a t i c a l foundation. 2). W e are released from the b u r d e n of learning the expensive F R A M E m o d e l i n feature pursuit, m o d e l selection a n d texture synthesis. In this paper, a n efficient M a r k o v chain M o n t e C a r l o a l g o r i t h m is proposed for s a m p l i n g Julesz ensembles. T h e a l g o r i t h m generates r a n d o m texture images by m o v i n g along the directions of filter coefficients a n d thus extends the t r a d i t i o n a l single site G i b b s sampler. T h i s paper also compares four p o p u l a r statistical measures i n the literature, namely, moments, rectified functions, m a r g i n a l histograms a n d joint histograms of linear filter responses i n terms of their descriptive abilities. O u r experiments suggest that a s m a l l number of bins i n m a r g i n a l histograms are sufficient for c a p t u r i n g a variety of texture patterns. W e illustrate our theory a n d a l g o r i t h m by successfully synthesizing a number of n a t u r a l textures. Keywords: G i b b s ensemble, Julesz ensemble, texture modeling, texture synthesis, M a r k o v chain M o n t e C a r l o . Song C h u n Z h u a n d X i u W e n L i u are w i t h the Department of C o m p u t e r a n d Informa- t i o n Sciences, T h e O h i o State University, C o l u m b u s , O H 43210. Y i n g N i a n W u is w i t h the Department of Statistics, U n i v e r s i t y of C a l i f o r n i a , Los Angeles, C A 90095.