Recently, fitted Q-iteration (FQI) based methods have become more popular due to their increased sample efficiency, a more stable learning process and the higher quality of the resulting policy. However, these methods remain hard to use for continuous action spaces which frequently occur in real-world tasks, e.g., in robotics and other technical applications. The greedy action selection commonly used for the policy improvement step is particularly problematic as it is expensive for continuous actions, can cause an unstable learning process, introduces an optimization bias and results in highly non-smooth policies unsuitable for real-world systems. In this paper, we show that by using a soft-greedy action selection the policy improvement step used in FQI can be simplified to an inexpensive advantage-weighted regression. With this result, we are able to derive a new, computationally efficient FQI algorithm which can even deal with high dimensional action spaces.

Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations and hence support interpretability. Unfortunately, L1-norm MKL is hardly observed to outperform trivial baselines in practical applications. To allow for robust kernel mixtures, we generalize MKL to arbitrary Lp-norms. We devise new insights on the connection between several existing MKL formulations and develop two efficient interleaved optimization strategies for arbitrary p>1. Empirically, we demonstrate that the interleaved optimization strategies are much faster compared to the traditionally used wrapper approaches. Finally, we apply Lp-norm MKL to real-world problems from computational biology, showing that non-sparse MKL achieves accuracies that go beyond the state-of-the-art.

Orthogonal matching pursuit (OMP) is a widely used greedy algorithm for recovering sparse vectors from linear measurements. A well-known analysis of Tropp and Gilbert shows that OMP can recover a k-sparse n-dimensional real vector from m = 4k log(n) noise-free random linear measurements with a probability that goes to one as n goes to infinity. This work shows strengthens this result by showing that a lower number of measurements, m = 2k log(n-k), is in fact sufficient for asymptotic recovery. Moreover, this number of measurements is also sufficient for detection of the sparsity pattern (support) of the vector with measurement errors provided the signal-to-noise ratio (SNR) scales to infinity. The scaling m = 2k log(n-k) exactly matches the number of measurements required by the more complex lasso for signal recovery.

Imaging techniques such as optical imaging of intrinsic signals, 2-photon calcium imaging and voltage sensitive dye imaging can be used to measure the functional organization of visual cortex across different spatial scales. Here, we present Bayesian methods based on Gaussian processes for extracting topographic maps from functional imaging data. In particular, we focus on the estimation of orientation preference maps (OPMs) from intrinsic signal imaging data. We model the underlying map as a bivariate Gaussian process, with a prior covariance function that reflects known properties of OPMs, and a noise covariance adjusted to the data. The posterior mean can be interpreted as an optimally smoothed estimate of the map, and can be used for model based interpolations of the map from sparse measurements. By sampling from the posterior distribution, we can get error bars on statistical properties such as preferred orientations, pinwheel locations or -counts. Finally, the use of an explicit probabilistic model facilitates interpretation of parameters and provides the basis for decoding studies. We demonstrate our model both on simulated data and on intrinsic signaling data from ferret visual cortex.

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data.

Graph clustering methods such as spectral clustering are defined for general weighted graphs. In machine learning, however, data often is not given in form of a graph, but in terms of similarity (or distance) values between points. In this case, first a neighborhood graph is constructed using the similarities between the points and then a graph clustering algorithm is applied to this graph.

With the advent of the Internet it is now possible to collect hundreds of millions of images. These images come with varying degrees of label information. ``Clean labels can be manually obtained on a small fraction, ``noisy labels may be extracted automatically from surrounding text, while for most images there are no labels at all. Semi-supervised learning is a principled framework for combining these different label sources. However, it scales polynomially with the number of images, making it impractical for use on gigantic collections with hundreds of millions of images and thousands of classes. In this paper we show how to utilize recent results in machine learning to obtain highly efficient approximations for semi-supervised learning that are linear in the number of images.  Specifically, we use the convergence of the eigenvectors of the normalized graph Laplacian to eigenfunctions of weighted Laplace-Beltrami operators. We combine this with a label sharing framework obtained from Wordnet to propagate label information to classes lacking manual annotations. Our algorithm enables us to apply semi-supervised learning to a database of 80 million images with 74 thousand classes.

Almost all successful machine learning algorithms and cognitive models require powerful representations capturing the features that are relevant to a particular problem. We draw on recent work in nonparametric Bayesian statistics to define a rational model of human feature learning that forms a featural representation from raw sensory data without pre-specifying the number of features. By comparing how the human perceptual system and our rational model use distributional and category information to infer feature representations, we seek to identify some of the forces that govern the process by which people separate and combine sensory primitives to form features.

We describe an application of probabilistic modeling and inference technology to the problem of analyzing sensor data in the setting of an intensive care unit (ICU). In particular, we consider the arterial-line blood pressure sensor, which is subject to frequent data artifacts that cause false alarms in the ICU and make the raw data almost useless for automated decision making. The problem is complicated by the fact that the sensor data are averaged over fixed intervals whereas the events causing data artifacts may occur at any time and often have durations significantly shorter than the data collection interval. We show that careful modeling of the sensor, combined with a general technique for detecting sub-interval events and estimating their duration, enables detection of artifacts and accurate estimation of the underlying blood pressure values. Our model's performance identifying artifacts is superior to two other classifiers' and about as good as a physician's.

Synapses exhibit an extraordinary degree of short-term malleability, with release probabilities and effective synaptic strengths changing markedly over multiple timescales. From the perspective of a fixed computational operation in a network, this seems like a most unacceptable degree of added noise. We suggest an alternative theory according to which short term synaptic plasticity plays a normatively-justifiable role. This theory starts from the commonplace observation that the spiking of a neuron is an incomplete, digital, report of the analog quantity that contains all the critical information, namely its membrane potential. We suggest that one key task for a synapse is to solve the inverse problem of estimating the pre-synaptic membrane potential from the spikes it receives and prior expectations, as in a recursive filter. We show that short-term synaptic depression has canonical dynamics which closely resemble those required for optimal estimation, and that it indeed supports high quality estimation. Under this account, the local postsynaptic potential and the level of synaptic resources track the (scaled) mean and variance of the estimated presynaptic membrane potential. We make experimentally testable predictions for how the statistics of subthreshold membrane potential fluctuations and the form of spiking non-linearity should be related to the properties of short-term plasticity in any particular cell type.