The replica method is a non-rigorous but widely-used technique from statistical physics used in the asymptotic analysis of many large random nonlinear problems. This paper applies the replica method to non-Gaussian MAP estimation. It is shown that with large random linear measurements and Gaussian noise, the asymptotic behavior of the MAP estimate of an n-dimensional vector ``decouples as n scalar MAP estimators. The result is a counterpart to Guo and Verdus replica analysis on MMSE estimation. The replica MAP analysis can be readily applied to many estimators used in compressed sensing, including basis pursuit, lasso, linear estimation with thresholding and zero-norm estimation. In the case of lasso estimation, the scalar estimator reduces to a soft-thresholding operator and for zero-norm estimation it reduces to a hard-threshold. Among other benefits, the replica method provides a computationally tractable method for exactly computing various performance metrics including MSE and sparsity recovery.

This paper studies global ranking problem by learning to rank methods. Conventional learning to rank methods are usually designed for `local ranking', in the sense that the ranking model is defined on a single object, for example, a document in information retrieval. For many applications, this is a very loose approximation. Relations always exist between objects and it is better to define the ranking model as a function on all the objects to be ranked (i.e., the relations are also included). This paper refers to the problem as global ranking and proposes employing a Continuous Conditional Random Fields (CRF) for conducting the learning task. The Continuous CRF model is defined as a conditional probability distribution over ranking scores of objects conditioned on the objects. It can naturally represent the content information of objects as well as the relation information between objects, necessary for global ranking. Taking two specific information retrieval tasks as examples, the paper shows how the Continuous CRF method can perform global ranking better than baselines.

Motor primitives or motion templates have become an important concept for both modeling human motor control as well as generating robot behaviors using imitation learning. Recent impressive results range from humanoid robot movement generation to timing models of human motions. The automatic generation of skill libraries containing multiple motion templates is an important step in robot learning. Such a skill learning system needs to cluster similar movements together and represent each resulting motion template as a generative model which is subsequently used for the execution of the behavior by a robot system. In this paper, we show how human trajectories captured as multidimensional time-series can be clustered using Bayesian mixtures of linear Gaussian state-space models based on the similarity of their dynamics. The appropriate number of templates is automatically determined by enforcing a parsimonious parametrization. As the resulting model is intractable, we introduce a novel approximation method based on variational Bayes, which is especially designed to enable the use of efficient inference algorithms. On recorded human Balero movements, this method is not only capable of finding reasonable motion templates but also yields a generative model which works well in the execution of this complex task on a simulated anthropomorphic SARCOS arm.

Humans are typically able to infer how many objects their environment contains and to recognize when the same object is encountered twice. We present a simple statisticalmodel that helps to explain these abilities and evaluate it in three behavioral experiments. Our first experiment suggests that humans rely on prior knowledge when deciding whether an object token has been previously encountered. Oursecond and third experiments suggest that humans can infer how many objects they have seen and can learn about categories and their properties even when they are uncertain about which tokens are instances of the same object. From an early age, humans and other animals [1] appear to organize the flux of experience into a series of encounters with discrete and persisting objects.

Psychophysical experiments show that humans are better at perceiving rotation and expansion than translation. These findings are inconsistent with standard models of motion integration which predict best performance for translation [6]. To explain this discrepancy, our theory formulates motion perception at two levels of inference: we first perform model selection between the competing models (e.g. translation, rotation, and expansion) and then estimate the velocity using the selected model. We define novel prior models for smooth rotation and expansion using techniques similar to those in the slow-and-smooth model [17] (e.g. Green functions of differential operators). The theory gives good agreement with the trends observed in human experiments.

Continuous-time Markov chains are used to model systems in which transitions between states as well as the time the system spends in each state are random. Many computational problems related to such chains have been solved, including determining state distributions as a function of time, parameter estimation, and control. However, the problem of inferring most likely trajectories, where a trajectory is a sequence of states as well as the amount of time spent in each state, appears unsolved. We study three versions of this problem: (i) an initial value problem, in which an initial state is given and we seek the most likely trajectory until a given final time, (ii) a boundary value problem, in which initial and final states and times are given, and we seek the most likely trajectory connecting them, and (iii) trajectory inference under partial observability, analogous to finding maximum likelihood trajectories for hidden Markov models. We show that maximum likelihood trajectories are not always well-defined, and describe a polynomial time test for well-definedness. When well-definedness holds, we show that each of the three problems can be solved in polynomial time, and we develop efficient dynamic programming algorithms for doing so.

Many interesting problems, including Bayesian network structure-search, can be cast in terms of finding the optimum value of a function over the space of graphs. However, this function is often expensive to compute exactly. We here present a method derived from the study of reproducing-kernel Hilbert spaces which takes advantage of the regular structure of the space of all graphs on a fixed number of nodes to obtain approximations to the desired function quickly and with reasonable accuracy. We then test this method on both a small testing set and a real-world Bayesian network; the results suggest that not only is this method reasonably accurate, but that the BDe score itself varies quadratically over the space of all graphs.

A central hypothesis about early visual processing is that it represents inputs in a coordinate system matched to the statistics of natural scenes. Simple versions of this lead to Gabor-like receptive fields and divisive gain modulation from local surrounds; these have led to influential neural and psychological models of visual processing. However, these accounts are based on an incomplete view of the visual context surrounding each point. Here, we consider an approximate model of linear and non-linear correlations between the responses of spatially distributed Gabor-like receptive fields, which, when trained on an ensemble of natural scenes, unifies a range of spatial context effects. The full model accounts for neural surround data in primary visual cortex (V1), provides a statistical foundation for perceptual phenomena associated with Lis (2002) hypothesis that V1 builds a saliency map, and fits data on the tilt illusion.

When individuals independently recollect events or retrieve facts from memory, how can we aggregate these retrieved memories to reconstruct the actual set of events or facts? In this research, we report the performance of individuals in a series of general knowledge tasks, where the goal is to reconstruct from memory the order of historic events, or the order of items along some physical dimension. We introduce two Bayesian models for aggregating order information based on a Thurstonian approach and Mallows model. Both models assume that each individuals reconstruction is based on either a random permutation of the unobserved ground truth, or by a pure guessing strategy. We apply MCMC to make inferences about the underlying truth and the strategies employed by individuals. The models demonstrate a wisdom of crowds" effect, where the aggregated orderings are closer to the true ordering than the orderings of the best individual."

In many domains, humans appear to combine perceptual cues in a near-optimal, probabilistic fashion: two noisy pieces of information tend to be combined linearly with weights proportional to the precision of each cue. Here we present a case where structural information plays an important role. The presence of a background cue gives rise to the possibility of occlusion, and places a soft constraint on the location of a target – in effect propelling it forward. We present an ideal observer model of depth estimation for this situation where structural or ordinal information is important and then fit the model to human data from a stereo-matching task. To test whether subjects are truly using ordinal cues in a probabilistic manner we then vary the uncertainty of the task. We find that the model accurately predicts shifts in subject’s behavior. Our results indicate that the nervous system estimates depth ordering in a probabilistic fashion and estimates the structure of the visual scene during depth perception.