Nonparametric Bayesian models are often based on the assumption that the objects being modeled are exchangeable. While appropriate in some applications (e.g., bag-of-words models for documents), exchangeability is sometimes assumed simply for computational reasons; non-exchangeable models might be a better choice for applications based on subject matter. Drawing on ideas from graphical models and phylogenetics, we describe a non-exchangeable prior for a class of nonparametric latent feature models that is nearly as efficient computationally as its exchangeable counterpart. Our model is applicable to the general setting in which the dependencies between objects can be expressed using a tree, where edge lengths indicate the strength of relationships. We demonstrate an application to modeling probabilistic choice.

Confidence measures for the generalization error are crucial when small training samples are used to construct classifiers. A common approach is to estimate the generalization error by resampling and then assume the resampled estimator follows a known distribution to form a confidence set [Kohavi 1995, Martin 1996,Yang 2006]. Alternatively, one might bootstrap the resampled estimator of the generalization error to form a confidence set. Unfortunately, these methods do not reliably provide sets of the desired confidence. The poor performance appears to be due to the lack of smoothness of the generalization error as a function of the learned classifier. This results in a non-normal distribution of the estimated generalization error. We construct a confidence set for the generalization error by use of a smooth upper bound on the deviation between the resampled estimate and generalization error. The confidence set is formed by bootstrapping this upper bound. In cases in which the approximation class for the classifier can be represented as a parametric additive model, we provide a computationally efficient algorithm. This method exhibits superior performance across a series of test and simulated data sets.

We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters, de ned as well-connected subsets of vertices. The decomposition is based on a statistical description which encourages clusters to be well connected and few in number. Inference is carried out using a variational approximation. Clique matrices also play a natural role in parameterising positive de nite matrices under zero constraints on elements of the matrix. We show that clique matrices can parameterise all positive de nite matrices restricted according to a decomposable graph and form a structured Factor Analysis approximation in the non-decomposable case.

A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in the family of directed out-tree graphs which leads to efficient Bayesian inference. The latent likelihood of the data and its gradients are computable in closed form via Tutte's directed matrix tree theorem using determinants and inverses of the out-Laplacian. This novel likelihood subsumes iid likelihood, is exchangeable and yields efficient unsupervised and semi-supervised learning algorithms. In addition to handling taxonomy and phylogenetic datasets the out-tree assumption performs surprisingly well as a semi-parametric density estimator on standard iid datasets. Experiments with unsupervised and semisupervised learning are shown on various UCI and taxonomy datasets.

Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief propagation (LBP) can suffer from poor convergence. In this paper, we provide a different approach for combining MRF learning and Bethe approximation. We consider the dual of maximum likelihood Markov network learning - maximizing entropy with moment matching constraints - and then approximate both the objective and the constraints in the resulting optimization problem. Unlike previous work along these lines (Teh & Welling, 2003), our formulation allows parameter sharing between features in a general log-linear model, parameter regularization and conditional training. We show that piecewise training (Sutton & McCallum, 2005) is a very restricted special case of this formulation. We study two optimization strategies: one based on a single convex approximation and one that uses repeated convex approximations. We show results on several real-world networks that demonstrate that these algorithms can significantly outperform learning with loopy and piecewise. Our results also provide a framework for analyzing the trade-offs of different relaxations of the entropy objective and of the constraints.

This paper presents a natural extension of stagewise ranking to the the case of infinitely many items. We introduce the infinite generalized Mallows model (IGM), describe its properties and give procedures to estimate it from data. For estimation of multimodal distributions we introduce the Exponential-Blurring-Mean-Shift nonparametric clustering algorithm. The experiments highlight the properties of the new model and demonstrate that infinite models can be simple, elegant and practical.

Assume that cause-effect relationships between variables can be described as a directed acyclic graph and the corresponding linear structural equation model.We consider the identification problem of total effects in the presence of latent variables and selection bias between a treatment variable and a response variable. Pearl and his colleagues provided the back door criterion, the front door criterion (Pearl, 2000) and the conditional instrumental variable method (Brito and Pearl, 2002) as identifiability criteria for total effects in the presence of latent variables, but not in the presence of selection bias. In order to solve this problem, we propose new graphical identifiability criteria for total effects based on the identifiable factor models. The results of this paper are useful to identify total effects in observational studies and provide a new viewpoint to the identification conditions of factor models.

We derive a novel norm that corresponds to the tightest convex relaxation of sparsity combined with an $\ell_2$ penalty. We show that this new {\em $k$-support norm} provides a tighter relaxation than the elastic net and is thus a good replacement for the Lasso or the elastic net in sparse prediction problems. Through the study of the $k$-support norm, we also bound the looseness of the elastic net, thus shedding new light on it and providing justification for its use.

Agricultural research has been profited by technical advances such as automation, data mining. Today, data mining is used in a vast areas and many off-the-shelf data mining system products and domain specific data mining application soft wares are available, but data mining in agricultural soil datasets is a relatively a young research field. The large amounts of data that are nowadays virtually harvested along with the crops have to be analyzed and should be used to their full extent. This research aims at analysis of soil dataset using data mining techniques. It focuses on classification of soil using various algorithms available. Another important purpose is to predict untested attributes using regression technique, and implementation of automated soil sample classification.

This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is a "forward-backward" greedy procedure that -- uniquely -- operates on two distinct classes of objects. In particular, we organize our target sparse vectors as a matrix; our algorithm involves iterative addition and removal of both (a) individual elements, and (b) entire rows (corresponding to shared features), of the matrix. Analytically, we establish that our algorithm manages to recover the supports (exactly) and values (approximately) of the sparse vectors, under assumptions similar to existing approaches based on convex optimization. However, our algorithm has a much smaller computational complexity. Perhaps most interestingly, it is seen empirically to require visibly fewer samples. Ours represents the first attempt to extend greedy algorithms to the class of models that can only/best be represented by a combination of component structural assumptions (sparse and group-sparse, in our case).