We derive risk bounds for the randomized classifiers in Sample Compressions settings where the classifier-specification utilizes two sources of information viz. the compression set and the message string. By extending the recently proposed Occam’s Hammer principle to the data-dependent settings, we derive point-wise versions of the bounds on the stochastic sample compressed classifiers and also recover the corresponding classical PAC-Bayes bound. We further show how these compare favorably to the existing results.

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.

We present the Gaussian Process Density Sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a fixed density function that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We can also infer the hyperparameters of the Gaussian process. We compare this density modeling technique to several existing techniques on a toy problem and a skull-reconstruction task.

It has been established that the second-order stochastic gradient descent (2SGD) method can potentially achieve generalization performance as well as empirical optimum in a single pass (i.e., epoch) through the training examples. However, 2SGD requires computing the inverse of the Hessian matrix of the loss function, which is prohibitively expensive. This paper presents Periodic Step-size Adaptation (PSA), which approximates the Jacobian matrix of the mapping function and explores a linear relation between the Jacobian and Hessian to approximate the Hessian periodically and achieve near-optimal results in experiments on a wide variety of models and tasks.

Large, relational factor graphs with structure defined by first-order logic or other languages give rise to notoriously difficult inference problems. Because unrolling the structure necessary to represent distributions over all hypotheses has exponential blow-up, solutions are often derived from MCMC. However, because of limitations in the design and parameterization of the jump function, these sampling-based methods suffer from local minima|the system must transition through lower-scoring configurations before arriving at a better MAP solution. This paper presents a new method of explicitly selecting fruitful downward jumps by leveraging reinforcement learning (RL). Rather than setting parameters to maximize the likelihood of the training data, parameters of the factor graph are treated as a log-linear function approximator and learned with temporal difference (TD); MAP inference is performed by executing the resulting policy on held out test data. Our method allows efficient gradient updates since only factors in the neighborhood of variables affected by an action need to be computed|we bypass the need to compute marginals entirely. Our method provides dramatic empirical success, producing new state-of-the-art results on a complex joint model of ontology alignment, with a 48\% reduction in error over state-of-the-art in that domain.

In analogy to the PCA setting, the sparse PCA problem is often solved by iteratively alternating between two subtasks: cardinality-constrained rank-one variance maximization and matrix deflation. While the former has received a great deal of attention in the literature, the latter is seldom analyzed and is typically borrowed without justification from the PCA context. In this work, we demonstrate that the standard PCA deflation procedure is seldom appropriate for the sparse PCA setting. To rectify the situation, we first develop several heuristic deflation alternatives with more desirable properties. We then reformulate the sparse PCA optimization problem to explicitly reflect the maximum additional variance objective on each round. The result is a generalized deflation procedure that typically outperforms more standard techniques on real-world datasets.

The concave-convex procedure (CCCP) is a majorization-minimization algorithm that solves d.c. (difference of convex functions) programs as a sequence of convex programs. In machine learning, CCCP is extensively used in many learning algorithms like sparse support vector machines (SVMs), transductive SVMs, sparse principal component analysis, etc. Though widely used in many applications, the convergence behavior of CCCP has not gotten a lot of specific attention. Yuille and Rangarajan analyzed its convergence in their original paper, however, we believe the analysis is not complete. Although the convergence of CCCP can be derived from the convergence of the d.c. algorithm (DCA), their proof is more specialized and technical than actually required for the specific case of CCCP. In this paper, we follow a different reasoning and show how Zangwills global convergence theory of iterative algorithms provides a natural framework to prove the convergence of CCCP, allowing a more elegant and simple proof. This underlines Zangwills theory as a powerful and general framework to deal with the convergence issues of iterative algorithms, after also being used to prove the convergence of algorithms like expectation-maximization, generalized alternating minimization, etc. In this paper, we provide a rigorous analysis of the convergence of CCCP by addressing these questions: (i) When does CCCP find a local minimum or a stationary point of the d.c. program under consideration? (ii) When does the sequence generated by CCCP converge? We also present an open problem on the issue of local convergence of CCCP.

Language and image understanding are two major goals of artificial intelligence which can both be conceptually formulated in terms of parsing the input signal into a hierarchical representation. Natural language researchers have made great progress by exploiting the 1D structure of language to design efficient polynomialtime parsing algorithms. By contrast, the two-dimensional nature of images makes it much harder to design efficient image parsers and the form of the hierarchical representations is also unclear. Attempts to adapt representations and algorithms from natural language have only been partially successful. In this paper, we propose a Hierarchical Image Model (HIM) for 2D image parsing which outputs image segmentation and object recognition.