A common approach for handling the complexity and inherent ambiguities of 3D human pose estimation is to use pose priors learned from training data. Existing approaches however, are either too simplistic (linear), too complex to learn, or can only learn latent spaces from "simple data", i.e., single activities such as walking or running. In this paper, we present an efficient stochastic gradient descent algorithm that is able to learn probabilistic non-linear latent spaces composed of multiple activities. Furthermore, we derive an incremental algorithm for the online setting which can update the latent space without extensive relearning. We demonstrate the effectiveness of our approach on the task of monocular and multi-view tracking and show that our approach outperforms the state-of-the-art.

Nonparametric Bayesian methods are developed for analysis of multi-channel spike-train data, with the feature learning and spike sorting performed jointly. The feature learning and sorting are performed simultaneously across all channels. Dictionary learning is implemented via the beta-Bernoulli process, with spike sorting performed via the dynamic hierarchical Dirichlet process (dHDP), with these two models coupled. The dHDP is augmented to eliminate refractory-period violations, it allows the "appearance" and "disappearance" of neurons over time, and it models smooth variation in the spike statistics.

We propose a novel inference framework for finding maximal cliques in a weighted graph that satisfy hard constraints. The constraints specify the graph nodes that must belong to the solution as well as mutual exclusions of graph nodes, i.e., sets of nodes that cannot belong to the same solution. The proposed inference is based on a novel particle filter algorithm with state permeations. We apply the inference framework to a challenging problem of learning part-based, deformable object models. Two core problems in the learning framework, matching of image patches and finding salient parts, are formulated as two instances of the problem of finding maximal cliques with hard constraints. Our learning framework yields discriminative part based object models that achieve very good detection rate, and outperform other methods on object classes with large deformation.

Many nonparametric regressors were recently shown to converge at rates that depend only on the intrinsic dimension of data. These regressors thus escape the curse of dimension when high-dimensional data has low intrinsic dimension (e.g. a manifold). We show that $k$-NN regression is also adaptive to intrinsic dimension. In particular our rates are local to a query $x$ and depend only on the way masses of balls centered at $x$ vary with radius. Furthermore, we show a simple way to choose $k = k(x)$ locally at any $x$ so as to nearly achieve the minimax rate at $x$ in terms of the unknown intrinsic dimension in the vicinity of $x$. We also establish that the minimax rate does not depend on a particular choice of metric space or distribution, but rather that this minimax rate holds for any metric space and doubling measure.

Multi-task learning (MTL) learns multiple related tasks simultaneously to improve generalization performance. Alternating structure optimization (ASO) is a popular MTL method that learns a shared low-dimensional predictive structure on hypothesis spaces from multiple related tasks. It has been applied successfully in many real world applications. As an alternative MTL approach, clustered multi-task learning (CMTL) assumes that multiple tasks follow a clustered structure, i.e., tasks are partitioned into a set of groups where tasks in the same group are similar to each other, and that such a clustered structure is unknown a priori. The objectives in ASO and CMTL differ in how multiple tasks are related. Interestingly, we show in this paper the equivalence relationship between ASO and CMTL, providing significant new insights into ASO and CMTL as well as their inherent relationship. The CMTL formulation is non-convex, and we adopt a convex relaxation to the CMTL formulation. We further establish the equivalence relationship between the proposed convex relaxation of CMTL and an existing convex relaxation of ASO, and show that the proposed convex CMTL formulation is significantly more efficient especially for high-dimensional data. In addition, we present three algorithms for solving the convex CMTL formulation. We report experimental results on benchmark datasets to demonstrate the efficiency of the proposed algorithms.

In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex forms and better properties than traditional Cauchy and double exponential priors. We first propose a new class of normal scale mixtures through a novel generalized beta distribution that encompasses many interesting priors as special cases. This encompassing framework should prove useful in comparing competing priors, considering properties and revealing close connections. We then develop a class of variational Bayes approximations through the new hierarchy presented that will scale more efficiently to the types of truly massive data sets that are now encountered routinely.

The object people perceive in an image can depend on its orientation relative to the scene it is in (its reference frame). For example, the images of the symbols $\times$ and $+$ differ by a 45 degree rotation. Although real scenes have multiple images and reference frames, psychologists have focused on scenes with only one reference frame. We propose an ideal observer model based on nonparametric Bayesian statistics for inferring the number of reference frames in a scene and their parameters. When an ambiguous image could be assigned to two conflicting reference frames, the model predicts two factors should influence the reference frame inferred for the image: The image should be more likely to share the reference frame of the closer object ({\em proximity}) and it should be more likely to share the reference frame containing the most objects ({\em alignment}). We confirm people use both cues using a novel methodology that allows for easy testing of human reference frame inference.

Discriminative learning when training and test data belong to different distributions is a challenging and complex task. Often times we have very few or no labeled data from the test or target distribution but may have plenty of labeled data from multiple related sources with different distributions. The difference in distributions may be both in marginal and conditional probabilities. Most of the existing domain adaptation work focuses on the marginal probability distribution difference between the domains, assuming that the conditional probabilities are similar. However in many real world applications, conditional probability distribution differences are as commonplace as marginal probability differences. In this paper we propose a two-stage domain adaptation methodology which combines weighted data from multiple sources based on marginal probability differences (first stage) as well as conditional probability differences (second stage), with the target domain data. The weights for minimizing the marginal probability differences are estimated independently, while the weights for minimizing conditional probability differences are computed simultaneously by exploiting the potential interaction among multiple sources. We also provide a theoretical analysis on the generalization performance of the proposed multi-source domain adaptation formulation using the weighted Rademacher complexity measure. Empirical comparisons with existing state-of-the-art domain adaptation methods using three real-world datasets demonstrate the effectiveness of the proposed approach.

We consider the minimization of a convex objective function defined on a Hilbert space, which is only available through unbiased estimates of its gradients. This problem includes standard machine learning algorithms such as kernel logistic regression and least-squares regression, and is commonly referred to as a stochastic approximation problem in the operations research community. We provide a non-asymptotic analysis of the convergence of two well-known algorithms, stochastic gradient descent (a.k.a.~Robbins-Monro algorithm) as well as a simple modification where iterates are averaged (a.k.a.~Polyak-Ruppert averaging). Our analysis suggests that a learning rate proportional to the inverse of the number of iterations, while leading to the optimal convergence rate in the strongly convex case, is not robust to the lack of strong convexity or the setting of the proportionality constant. This situation is remedied when using slower decays together with averaging, robustly leading to the optimal rate of convergence. We illustrate our theoretical results with simulations on synthetic and standard datasets.

Recently, there has been substantial interest in using large amounts of unlabeled data to learn word representations which can then be used as features in supervised classifiers for NLP tasks. However, most current approaches are slow to train, do not model the context of the word, and lack theoretical grounding. In this paper, we present a new learning method, Low Rank Multi-View Learning (LR-MVL) which uses a fast spectral method to estimate low dimensional context-specific word representations from unlabeled data. These representation features can then be used with any supervised learner. LR-MVL is extremely fast, gives guaranteed convergence to a global optimum, is theoretically elegant, and achieves state-ofthe-art performanceon named entity recognition (NER) and chunking problems.