A weighted graph is used as an underlying structure of many algorithms like semi-supervised learning and spectral clustering. The edge weights are usually deter-mined by a single similarity measure, but it often hard if not impossible to capture all relevant aspects of similarity when using a single similarity measure. In par-ticular, in the case of visual object matching it is beneficial to integrate different similarity measures that focus on different visual representations. In this paper, a novel approach to integrate multiple similarity measures is pro-posed. First pairs of similarity measures are combined with a diffusion process on their tensor product graph (TPG). Hence the diffused similarity of each pair of ob-jects becomes a function of joint diffusion of the two original similarities, which in turn depends on the neighborhood structure of the TPG. We call this process Fusion with Diffusion (FD). However, a higher order graph like the TPG usually means significant increase in time complexity. This is not the case in the proposed approach. A key feature of our approach is that the time complexity of the dif-fusion on the TPG is the same as the diffusion process on each of the original graphs, Moreover, it is not necessary to explicitly construct the TPG in our frame-work. Finally all diffused pairs of similarity measures are combined as a weighted sum. We demonstrate the advantages of the proposed approach on the task of visual tracking, where different aspects of the appearance similarity between the target object in frame t and target object candidates in frame t+1 are integrated. The obtained method is tested on several challenge video sequences and the experimental results show that it outperforms state-of-the-art tracking methods.

We introduce a new prior for use in Nonparametric Bayesian Hierarchical Clustering. The prior is constructed by marginalizing out the time information of Kingman’s coalescent, providing a prior over tree structures which we call the Time-Marginalized Coalescent (TMC). This allows for models which factorize the tree structure and times, providing two benefits: more flexible priors may be constructed and more efficient Gibbs type inference can be used. We demonstrate this on an example model for density estimation and show the TMC achieves competitive experimental results.

The use of machine learning algorithms frequently involves careful tuning of learning parameters and model hyperparameters. Unfortunately, this tuning is often a “black art” requiring expert experience, rules of thumb, or sometimes brute-force search. There is therefore great appeal for automatic approaches that can optimize the performance of any given learning algorithm to the problem at hand. In this work, we consider this problem through the framework of Bayesian optimization, in which a learning algorithm’s generalization performance is modeled as a sample from a Gaussian process (GP). We show that certain choices for the nature of the GP, such as the type of kernel and the treatment of its hyperparameters, can play a crucial role in obtaining a good optimizer that can achieve expert-level performance. We describe new algorithms that take into account the variable cost (duration) of learning algorithm experiments and that can leverage the presence of multiple cores for parallel experimentation. We show that these proposed algorithms improve on previous automatic procedures and can reach or surpass human expert-level optimization for many algorithms including Latent Dirichlet Allocation, Structured SVMs and convolutional neural networks.

In this paper, we consider the problem of debugging large pipelines by human labeling. We represent the execution of a pipeline using a directed acyclic graph of AND and OR nodes, where each node represents a data item produced by some operator in the pipeline. We assume that each operator assigns a confidence to each of its output data. We want to reduce the uncertainty in the output by issuing queries to a human expert, where a query consists of checking if a given data item is correct. In this paper, we consider the problem of asking the optimal set of queries to minimize the resulting output uncertainty. We perform a detailed evaluation of the complexity of the problem for various classes of graphs. We give efficient algorithms for the problem for trees, and show that, for a general dag, the problem is intractable.

We introduce a class of discrete divergences on sets (equivalently binary vectors) that we call the submodular-Bregman divergences. We consider two kinds, defined either from tight modular upper or tight modular lower bounds of a submodular function. We show that the properties of these divergences are analogous to the (standard continuous) Bregman divergence. We demonstrate how they generalize many useful divergences, including the weighted Hamming distance, squared weighted Hamming, weighted precision, recall, conditional mutual information, and a generalized KL-divergence on sets. We also show that the generalized Bregman divergence on the Lovász extension of a submodular function, which we call the Lovász-Bregman divergence, is a continuous extension of a submodular Bregman divergence. We point out a number of applications, and in particular show that a proximal algorithm defined through the submodular Bregman divergence provides aframework for many mirror-descent style algorithms related to submodular function optimization. We also show that a generalization of the k-means algorithm using the Lovász Bregman divergence is natural in clustering scenarios where ordering is important. A unique property of this algorithm is that computing the mean ordering is extremely efficient unlike other order based distance measures.

Sparse learning models typically combine a smooth loss with a nonsmooth penalty, such as trace norm. Although recent developments in sparse approximation have offered promising solution methods, current approaches either apply only to matrix-norm constrained problems or provide suboptimal convergence rates. In this paper, we propose a boosting method for regularized learning that guarantees $\epsilon$ accuracy within $O(1/\epsilon)$ iterations. Performance is further accelerated by interlacing boosting with fixed-rank local optimization---exploiting a simpler local objective than previous work. The proposed method yields state-of-the-art performance on large-scale problems. We also demonstrate an application to latent multiview learning for which we provide the first efficient weak-oracle.

Pedigrees, or family trees, are directed graphs used to identify sites of the genome that are correlated with the presence or absence of a disease. With the advent of genotyping and sequencing technologies, there has been an explosion in the amount of data available, both in the number of individuals and in the number of sites. Some pedigrees number in the thousands of individuals. Meanwhile, analysis methods have remained limited to pedigrees of <100 individuals which limits analyses to many small independent pedigrees. Disease models, such those used for the linkage analysis log-odds (LOD) estimator, have similarly been limited. This is because linkage anlysis was originally designed with a different task in mind, that of ordering the sites in the genome, before there were technologies that could reveal the order. LODs are difficult to interpret and nontrivial to extend to consider interactions among sites. These developments and difficulties call for the creation of modern methods of pedigree analysis. Drawing from recent advances in graphical model inference and transducer theory, we introduce a simple yet powerful formalism for expressing genetic disease models. We show that these disease models can be turned into accurate and efficient estimators. The technique we use for constructing the variational approximation has potential applications to inference in other large-scale graphical models. This method allows inference on larger pedigrees than previously analyzed in the literature, which improves disease site prediction.

One of the enduring challenges in Markov chain Monte Carlo methodology is the development of proposal mechanisms to make moves distant from the current point, that are accepted with high probability and at low computational cost. The recent introduction of locally adaptive MCMC methods based on the natural underlying Riemannian geometry of such models goes some way to alleviating these problems for certain classes of models for which the metric tensor is analytically tractable, however computational efficiency is not assured due to the necessity of potentially high-dimensional matrix operations at each iteration. In this paper we firstly investigate a sampling-based approach for approximating the metric tensor and suggest a valid MCMC algorithm that extends the applicability of Riemannian Manifold MCMC methods to statistical models that do not admit an analytically computable metric tensor. Secondly, we show how the approximation scheme we consider naturally motivates the use of l1 regularisation to improve estimates and obtain a sparse approximate inverse of the metric, which enables stable and sparse approximations of the local geometry to be made. We demonstrate the application of this algorithm for inferring the parameters of a realistic system of ordinary differential equations using a biologically motivated robust student-t error model, for which the expected Fisher Information is analytically intractable.

In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure over the space of adjacency matrices and VAR matrices which takes into account both sparsity and low rank properties of the matrices. Oracle inequalities are derived and illustrate the trade-offs in the choice of smoothing parameters when modeling the joint effect of sparsity and low rank property. The estimate is computed efficiently using proximal methods through a generalized forward-backward agorithm.

Linear Support Vector Machines (SVMs) have become very popular in vision as part of state-of-the-art object recognition and other classification tasks but require high dimensional feature spaces for good performance. Deep learning methods can find more compact representations but current methods employ multilayer perceptrons that require solving a difficult, non-convex optimization problem. We propose a deep non-linear classifier whose layers are SVMs and which incorporates random projection as its core stacking element. Our method learns layers of linear SVMs recursively transforming the original data manifold through a random projection of the weak prediction computed from each layer. Our method scales as linear SVMs, does not rely on any kernel computations or nonconvex optimization, and exhibits better generalization ability than kernel-based SVMs. This is especially true when the number of training samples is smaller than the dimensionality of data, a common scenario in many real-world applications. The use of random projections is key to our method, as we show in the experiments section, in which we observe a consistent improvement over previous --often more complicated-- methods on several vision and speech benchmarks.