We show that linear generalizations of Rescorla-Wagner can perform Maximum Likelihood estimation of the parameters of all generative models for causal reasoning. Our approach involves augmenting variables to deal with conjunctions of causes, similar to the agumented model of Rescorla. Our results involve genericity assumptions on the distributions of causes. If these assumptions are violated, for example for the Cheng causal power theory, then we show that a linear Rescorla-Wagner can estimate the parameters of the model up to a nonlinear transformtion. Moreover, a nonlinear Rescorla-Wagner is able to estimate the parameters directly to within arbitrary accuracy. Previous results can be used to determine convergence and to estimate convergence rates.

Spiking activity from neurophysiological experiments often exhibits dynamics beyond that driven by external stimulation, presumably reflecting the extensive recurrence of neural circuitry. Characterizing these dynamics may reveal important features of neural computation, particularly during internally-driven cognitive operations. For example, the activity of premotor cortex (PMd) neurons during an instructed delay period separating movement-target specification and a movementinitiation cue is believed to be involved in motor planning. We show that the dynamics underlying this activity can be captured by a lowdimensional nonlinear dynamical systems model, with underlying recurrent structure and stochastic point-process output.

The observed physiological dynamics of an infant receiving intensive care are affected by many possible factors, including interventions to the baby, the operation of the monitoring equipment and the state of health. The Factorial Switching Kalman Filter can be used to infer the presence of such factors from a sequence of observations, and to estimate the true values where these observations have been corrupted. We apply this model to clinical time series data and show it to be effective in identifying a number of artifactual and physiological patterns.

The classical Bayes rule computes the posterior model probability from the prior probability and the data likelihood. We generalize this rule to the case when the prior is a density matrix (symmetric positive definite and trace one) and the data likelihood a covariance matrix. The classical Bayes rule is retained as the special case when the matrices are diagonal. In the classical setting, the calculation of the probability of the data is an expected likelihood, where the expectation is over the prior distribution. In the generalized setting, this is replaced by an expected variance calculation where the variance is computed along the eigenvectors of the prior density matrix and the expectation is over the eigenvalues of the density matrix (which form a probability vector). The variances along any direction is determined by the covariance matrix. Curiously enough this expected variance calculation is a quantum measurement where the covariance matrix specifies the instrument and the prior density matrix the mixture state of the particle. We motivate both the classical and the generalized Bayes rule with a minimum relative entropy principle, where the Kullbach-Leibler version gives the classical Bayes rule and Umegaki's quantum relative entropy the new Bayes rule for density matrices.

We present a probabilistic generative model of entity relationships and their attributes that simultaneously discovers groups among the entities and topics among the corresponding textual attributes. Block-models of relationship data have been studied in social network analysis for some time. Here we simultaneously cluster in several modalities at once, incorporating the attributes (here, words) associated with certain relationships. Significantly, joint inference allows the discovery of topics to be guided by the emerging groups, and vice-versa. We present experimental results on two large data sets: sixteen years of bills put before the U.S. Senate, comprising their corresponding text and voting records, and thirteen years of similar data from the United Nations. We show that in comparison with traditional, separate latent-variable models for words, or Blockstructures for votes, the Group-Topic model's joint inference discovers more cohesive groups and improved topics.

Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g., smoothing, denoising, interpolation) on a new noisy observation. Working in the computation-limited setting, we analyze a joint method in which the same convex variational relaxation is used to construct an M-estimator for fitting parameters, and to perform approximate marginalization for the prediction step. The key result of this paper is that in the computation-limited setting, using an inconsistent parameter estimator (i.e., an estimator that returns the "wrong" model even in the infinite data limit) is provably beneficial, since the resulting errors can partially compensate for errors made by using an approximate prediction technique. En route to this result, we analyze the asymptotic properties of M-estimators based on convex variational relaxations, and establish a Lipschitz stability property that holds for a broad class of variational methods. We show that joint estimation/prediction based on the reweighted sum-product algorithm substantially outperforms a commonly used heuristic based on ordinary sum-product.

Humans are extremely adept at learning new skills by imitating the actions of others. A progression of imitative abilities has been observed in children, ranging from imitation of simple body movements to goalbased imitation based on inferring intent. In this paper, we show that the problem of goal-based imitation can be formulated as one of inferring goals and selecting actions using a learned probabilistic graphical model of the environment. We first describe algorithms for planning actions to achieve a goal state using probabilistic inference. We then describe how planning can be used to bootstrap the learning of goal-dependent policies by utilizing feedback from the environment. The resulting graphical model is then shown to be powerful enough to allow goal-based imitation. Using a simple maze navigation task, we illustrate how an agent can infer the goals of an observed teacher and imitate the teacher even when the goals are uncertain and the demonstration is incomplete.

An increasing number of projects in neuroscience requires the statistical analysis of high dimensional data sets, as, for instance, in predicting behavior from neural firing or in operating artificial devices from brain recordings in brain-machine interfaces. Linear analysis techniques remain prevalent in such cases, but classical linear regression approaches are often numerically too fragile in high dimensions. In this paper, we address the question of whether EMG data collected from arm movements of monkeys can be faithfully reconstructed with linear approaches from neural activity in primary motor cortex (M1). To achieve robust data analysis, we develop a full Bayesian approach to linear regression that automatically detects and excludes irrelevant features in the data, regularizing against overfitting. In comparison with ordinary least squares, stepwise regression, partial least squares, LASSO regression and a brute force combinatorial search for the most predictive input features in the data, we demonstrate that the new Bayesian method offers a superior mixture of characteristics in terms of regularization against overfitting, computational efficiency and ease of use, demonstrating its potential as a drop-in replacement for other linear regression techniques. As neuroscientific results, our analyses demonstrate that EMG data can be well predicted from M1 neurons, further opening the path for possible real-time interfaces between brains and machines.

We present a simple and scalable algorithm for large-margin estimation of structured models, including an important class of Markov networks and combinatorial models. We formulate the estimation problem as a convex-concave saddle-point problem and apply the extragradient method, yielding an algorithm with linear convergence using simple gradient and projection calculations. The projection step can be solved using combinatorial algorithms for min-cost quadratic flow. This makes the approach an efficient alternative to formulations based on reductions to a quadratic program (QP). We present experiments on two very different structured prediction tasks: 3D image segmentation and word alignment, illustrating the favorable scaling properties of our algorithm.

We measure the ability of human observers to predict the next datum in a sequence that is generated by a simple statistical process undergoing change at random points in time. Accurate performance in this task requires the identification of changepoints. We assess individual differences between observers both empirically, and using two kinds of models: a Bayesian approach for change detection and a family of cognitively plausible fast and frugal models. Some individuals detect too many changes and hence perform sub-optimally due to excess variability. Other individuals do not detect enough changes, and perform sub-optimally because they fail to notice short-term temporal trends.