We consider the problem of learning models of options for real-time abstract planning, in the setting where reward functions can be specified at any time and their expected returns must be efficiently computed. We introduce a new model for an option that is independent of any reward function, called the {\it universal option model (UOM)}. We prove that the UOM of an option can construct a traditional option model given a reward function, and the option-conditional return is computed directly by a single dot-product of the UOM with the reward function. We extend the UOM to linear function approximation, and we show it gives the TD solution of option returns and value functions of policies over options. We provide a stochastic approximation algorithm for incrementally learning UOMs from data and prove its consistency. We demonstrate our method in two domains. The first domain is document recommendation, where each user query defines a new reward function and a document's relevance is the expected return of a simulated random-walk through the document's references. The second domain is a real-time strategy game, where the controller must select the best game unit to accomplish dynamically-specified tasks. Our experiments show that UOMs are substantially more efficient in evaluating option returns and policies than previously known methods.

Locally weighted regression (LWR) was created as a nonparametric method that can approximate a wide range of functions, is computationally efficient, and can learn continually from very large amounts of incrementally collected data. As an interesting feature, LWR can regress on non-stationary functions, a beneficial property, for instance, in control problems. However, it does not provide a proper generative model for function values, and existing algorithms have a variety of manual tuning parameters that strongly influence bias, variance and learning speed of the results. Gaussian (process) regression, on the other hand, does provide a generative model with rather black-box automatic parameter tuning, but it has higher computational cost, especially for big data sets and if a non-stationary model is required. In this paper, we suggest a path from Gaussian (process) regression to locally weighted regression, where we retain the best of both approaches. Using a localizing function basis and approximate inference techniques, we build a Gaussian (process) regression algorithm of increasingly local nature and similar computational complexity to LWR. Empirical evaluations are performed on several synthetic and real robot datasets of increasing complexity and (big) data scale, and demonstrate that we consistently achieve on par or superior performance compared to current state-of-the-art methods while retaining a principled approach to fast incremental regression with minimal manual tuning parameters.

A popular approach to neural characterization describes neural responses in terms of a cascade of linear and nonlinear stages: a linear filter to describe stimulus integration, followed by a nonlinear function to convert the filter output to spike rate. However, real neurons respond to stimuli in a manner that depends on the nonlinear integration of excitatory and inhibitory synaptic inputs. Here we introduce a biophysically inspired point process model that explicitly incorporates stimulus-induced changes in synaptic conductance in a dynamical model of neuronal membrane potential. Our work makes two important contributions. First, on a theoretical level, it offers a novel interpretation of the popular generalized linear model (GLM) for neural spike trains. We show that the classic GLM is a special case of our conductance-based model in which the stimulus linearly modulates excitatory and inhibitory conductances in an equal and opposite “push-pull” fashion. Our model can therefore be viewed as a direct extension of the GLM in which we relax these constraints; the resulting model can exhibit shunting as well as hyperpolarizing inhibition, and time-varying changes in both gain and membrane time constant. Second, on a practical level, we show that our model provides a tractable model of spike responses in early sensory neurons that is both more accurate and more interpretable than the GLM. Most importantly, we show that we can accurately infer intracellular synaptic conductances from extracellularly recorded spike trains. We validate these estimates using direct intracellular measurements of excitatory and inhibitory conductances in parasol retinal ganglion cells. We show that the model fit to extracellular spike trains can predict excitatory and inhibitory conductances elicited by novel stimuli with nearly the same accuracy as a model trained directly with intracellular conductances.

Numerous algorithms are used for nonnegative matrix factorization under the assumption that the matrix is nearly separable. In this paper, we show how to make these algorithms scalable for data matrices that have many more rows than columns, so-called tall-and-skinny matrices." One key component to these improved methods is an orthogonal matrix transformation that preserves the separability of the NMF problem. Our final methods need to read the data matrix only once and are suitable for streaming, multi-core, and MapReduce architectures. We demonstrate the efficacy of these algorithms on terabyte-sized matrices from scientific computing and bioinformatics."

We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global maximum. PES codifies this intractable acquisition function in terms of the expected reduction in the differential entropy of the predictive distribution. This reformulation allows PES to obtain approximations that are both more accurate and efficient than other alternatives such as Entropy Search (ES). Furthermore, PES can easily perform a fully Bayesian treatment of the model hyperparameters while ES cannot. We evaluate PES in both synthetic and real-world applications, including optimization problems in machine learning, finance, biotechnology, and robotics. We show that the increased accuracy of PES leads to significant gains in optimization performance.

We describe a seriation algorithm for ranking a set of n items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a similarity matrix from pairwise comparisons, using seriation methods to reorder this matrix and construct a ranking. We first show that this spectral seriation algorithm recovers the true ranking when all pairwise comparisons are observed and consistent with a total order. We then show that ranking reconstruction is still exact even when some pairwise comparisons are corrupted or missing, and that seriation based spectral ranking is more robust to noise than other scoring methods. An additional benefit of the seriation formulation is that it allows us to solve semi-supervised ranking problems. Experiments on both synthetic and real datasets demonstrate that seriation based spectral ranking achieves competitive and in some cases superior performance compared to classical ranking methods.

We consider the problem of inferring direct neural network connections from Calcium imaging time series. Inverse covariance estimation has proven to be a fast and accurate method for learning macro- and micro-scale network connectivity in the brain and in a recent Kaggle Connectomics competition inverse covariance was the main component of several top ten solutions, including our own and the winning team's algorithm. However, the accuracy of inverse covariance estimation is highly sensitive to signal preprocessing of the Calcium fluorescence time series. Furthermore, brute force optimization methods such as grid search and coordinate ascent over signal processing parameters is a time intensive process, where learning may take several days and parameters that optimize one network may not generalize to networks with different size and parameters. In this paper we show how inverse covariance estimation can be dramatically improved using a simple convolution filter prior to applying sample covariance. Furthermore, these signal processing parameters can be learned quickly using a supervised optimization algorithm. In particular, we maximize a binomial log-likelihood loss function with respect to a convolution filter of the time series and the inverse covariance regularization parameter. Our proposed algorithm is relatively fast on networks the size of those in the competition (1000 neurons), producing AUC scores with similar accuracy to the winning solution in training time under 2 hours on a cpu. Prediction on new networks of the same size is carried out in less than 15 minutes, the time it takes to read in the data and write out the solution.

Hierarchical feed-forward networks have been successfully applied in object recognition. At each level of the hierarchy, features are extracted and encoded, followed by a pooling step. Within this processing pipeline, the common trend is to learn the feature coding templates, often referred as codebook entries, filters, or over-complete basis. Recently, an approach that apparently does not use templates has been shown to obtain very promising results. This is the second-order pooling (O2P). In this paper, we analyze O2P as a coding-pooling scheme. We find that at testing phase, O2P automatically adapts the feature coding templates to the input features, rather than using templates learned during the training phase. From this finding, we are able to bring common concepts of coding-pooling schemes to O2P, such as feature quantization. This allows for significant accuracy improvements of O2P in standard benchmarks of image classification, namely Caltech101 and VOC07.

In this paper, we derive theoretical bounds for the long-term influence of a node in an Independent Cascade Model (ICM). We relate these bounds to the spectral radius of a particular matrix and show that the behavior is sub-critical when this spectral radius is lower than 1. More specifically, we point out that, in general networks, the sub-critical regime behaves in O(sqrt(n)) where n is the size of the network, and that this upper bound is met for star-shaped networks. We apply our results to epidemiology and percolation on arbitrary networks, and derive a bound for the critical value beyond which a giant connected component arises. Finally, we show empirically the tightness of our bounds for a large family of networks.

We present an inference method for Gaussian graphical models when only pairwise distances of n objects are observed. Formally, this is a problem of estimating an n x n covariance matrix from the Mahalanobis distances dMH(xi, xj), where object xi lives in a latent feature space. We solve the problem in fully Bayesian fashion by integrating over the Matrix-Normal likelihood and a Matrix-Gamma prior; the resulting Matrix-T posterior enables network recovery even under strongly correlated features. Hereby, we generalize TiWnet, which assumes Euclidean distances with strict feature independence. In spite of the greatly increased flexibility, our model neither loses statistical power nor entails more computational cost. We argue that the extension is highly relevant as it yields significantly better results in both synthetic and real-world experiments, which is successfully demonstrated for a network of biological pathways in cancer patients.