The joint problem of time segmentation and recognition of sequential data into meaningful subsequences has attracted significant research in a variety of domains. The ability to automatically segment and classify data is a core technology for applications like speaker diarisation, finance, activity understanding, multimedia annotation and human-computer interaction. To date, the main proposed solutions have included sliding windows [1], the hidden Markov model (HMM) [2], conditional random fields [3] [4], and structural SVM [5], covering the spectrum of generative, discriminative and maximum-margin dynamic classifiers. Along with advancements in learning and inference, research has witnessed increasingly realistic datasets which are bridging the gap between lab and real applications [6] [7]. Nevertheless, important challenges such as model adaptation and dynamic class sets remain unresolved. We address both these limitations by an adaptive online model that can accommodate an unlimited (theoretically infinite) number of classes. In a nutshell, this is achieved by applying a Bayesian nonparametric model, the hierarchical Dirichlet process (HDP), as the prior for a hidden Markov model (a model known as HDP-HMM [8] [9]), and exploiting an adaptive learning rate for model adaptation. The proposed model provides an adaptive online learning approach for joint segmentation and recognition of sequential data 1 with incremental class sets and we refer to it as ADON HDP-HMM in the following.

We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the original data matrix, then one can recover a near optimal solution to the optimization problem by using the sketch. In particular, we use this approach to obtain sparse principal components and show that for \math{m} data points in \math{n} dimensions, \math{O(\epsilon^{-2}\tilde k\max\{m,n\})} elements gives an \math{\epsilon}-additive approximation to the sparse PCA problem (\math{\tilde k} is the stable rank of the data matrix). We demonstrate our algorithms extensively on image, text, biological and financial data. The results show that not only are we able to recover the sparse PCAs from the incomplete data, but by using our sparse sketch, the running time drops by a factor of five or more.

We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several graphical Markov models. Rules for comparing degree of association among the vertices of such Gaussian graphical models are also developed. We apply these rules to compare conditional dependencies on Gaussian trees. In particular for trees, we show that such dependence can be completely characterized by the length of the paths joining the dependent vertices to each other and to the vertices conditioned on. We also apply our results to postulate rules for model selection for polytree models. Our rules apply to mutual information of Gaussian random vectors as well.

We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also enables us to expand the possible space where the dimension reduction functions belong. Our formulation provides a unified framework so that the classical notions, such as covariance standardization, Mahalanobis distance, SIR and linear discriminant analysis, can be naturally and smoothly carried out in our enlarged space. This enlarged dimension reduction space also links to the linear discriminant space of Gaussian measures on a separable Hilbert space.

This paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete distribution. The probability of this event is referred to as the "missing mass". The impossibility result can then be stated as: the missing mass is not distribution-free PAC-learnable in relative error. The proof is semi-constructive and relies on a coupling argument using a dithered geometric distribution. This result formalizes the folklore that in order to predict rare events, one necessarily needs distributions with "heavy tails".

Community detection is a fundamental problem in network analysis which is made more challenging by overlaps between communities which often occur in practice. Here we propose a general, flexible, and interpretable generative model for overlapping communities, which can be thought of as a generalization of the degree-corrected stochastic block model. We develop an efficient spectral algorithm for estimating the community memberships, which deals with the overlaps by employing the K-medians algorithm rather than the usual K-means for clustering in the spectral domain. We show that the algorithm is asymptotically consistent when networks are not too sparse and the overlaps between communities not too large. Numerical experiments on both simulated networks and many real social networks demonstrate that our method performs very well compared to a number of benchmark methods for overlapping community detection.

Conditional restricted Boltzmann machines are undirected stochastic neural networks with a layer of input and output units connected bipartitely to a layer of hidden units. These networks define models of conditional probability distributions on the states of the output units given the states of the input units, parametrized by interaction weights and biases. We address the representational power of these models, proving results their ability to represent conditional Markov random fields and conditional distributions with restricted supports, the minimal size of universal approximators, the maximal model approximation errors, and on the dimension of the set of representable conditional distributions. We contribute new tools for investigating conditional probability models, which allow us to improve the results that can be derived from existing work on restricted Boltzmann machine probability models.

Graph matching is an increasingly important problem in inferential graph statistics, with applications across a broad spectrum of fields including computer vision ([38], [10]), shape matching and object recognition ([4], [7]), and biology and neuroscience ([22], [34], [37]), to name a few. The graph matching problem (GMP) seeks to find an alignment between the vertex sets of two graphs that best preserves common structure across graphs. Unfortunately, the GMP is inherently combinatorial, and no efficient exact graph matching algorithms are known. Indeed, even the simpler problem of determining if two graphs are isomorphic is famously of unknown complexity ([19], 1 [30]), and if the graphs are allowed to be loopy, weighted and directed, then the simplest version of GMP is equivalent to the NPhard quadratic assignment problem. Due to its wide applicability, there exist a vast number of approximating algorithms for GMP; see the paper "30 Years of Graph Matching in Pattern Recognition" ([11]) for an excellent survey of the existing literature.

Remember those charming smartphone ads a few years ago where people held conversations with Siri, Apple iOS' enchanting virtual assistant? The concept was innovative for operating the phone hands-free but not so helpful in searching the web on your behalf. Oftentimes, Siri comes up with entirely wrong answers, too many options or services only tangentially relevant to your inquiry. Asking for a modestly-priced tailor or an upscale sushi bar known for uni is too ambitious. She hears us, but she's not listening.

ABSTRACT Several efforts to predict student failure rate (SFR) at school accurately still remains a core problem area faced by many in the educational sector. The procedure for forecasting SFR are rigid and most often times require data scaling or conversion into binary form such as is the case of the logistic model which may lead to lose of information and effect size attenuation. Currently the application of Genetic Programming (GP) holds great promises and has produced tremendous positive results in different sectors. In this regard, this study developed GPSFARPS, a software application to provide a robust solution to the prediction of SFR using an evolutionary algorithm known as multi-gene genetic programming. The approach is validated by feeding a testing data set to the evolved GP models. Result obtained from GPSFARPS simulations show its unique ability to evolve a suitable failure rate expression with a fast convergence at 30 generations from a maximum specified generation of 500. The multigene system was also able to minimize the evolved model expression and accurately predict student failure rate using a subset of the original expression. Keywords: Genetic Programming, Student Failure Rate, Multi-Gene GP 1. INTRODUCTION SFR has always being and will continue to be a major concern to stakeholders in the educational sector.