Probabilistic Regularities Research Articles

Second-order cone programming with probabilistic regularization for robust adaptive beamforming.

Probabilistic regularization (PR) is introduced to make superdirective array beamforming robust against sensor characteristic mismatches. The objective is to enlarge the directivity while ensuring robustness with high probability. The PR problem is solved via the second-order cone programming where the regularization parameter is chosen through a statistical analysis of the system perturbations, based on Monte Carlo simulations. Experiments are carried out on a miniaturized 3 × 3 uniform rectangular array without calibration. The results show that for this particular array, the PR method is robust to sensor mismatches and achieves a higher level of directivity compared with other robust adaptive beamforming approaches.

Repelling a Prussian charge with a solution to a paradox of Dubins

Pruss (Thought 1:81–89, 2012) uses an example of Lester Dubins to argue against the claim that appealing to hyperreal-valued probabilities saves probabilistic regularity from the objection that in continuum outcome-spaces and with standard probability functions all save countably many possibilities must be assigned probability 0. Dubins’s example seems to show that merely finitely additive standard probability functions allow reasoning to a foregone conclusion, and Pruss argues that hyperreal-valued probability functions are vulnerable to the same charge. However, Pruss’s argument relies on the rule of conditionalisation, but I show that in examples like Dubins’s involving nonconglomerable probabilities, conditionalisation is self-defeating.

Probabilistic regularization of Fredholm integral equations of the first kind

The main purpose of this paper is to focus on various issues inherent to the regularization theory of Fredholm integral equations of the first kind. Particular attention is devoted to the probabilistic approach to regularization, and a regularizing algorithm based on statistical methods is then proposed and tested on examples. The information theory approach is studied from two different viewpoints: the first approach is the standard one based on probability theory; the second one is formulated, in analogy with communication theory, in terms of the $\varepsilon $-capacity in the sense elaborated by Kolmogorov and his school. The classical problem of the resolving power in optics is then used to exemplify the relation between these two approaches.

A Mathematical Linguistic Approach to Rebus

The aim of this paper is the investigation of some combinatorial aspects of written language, within the framework determined by the well-known game of crossword puzzles. Various types of probabilistic regularities appearing in such puzzles reveal some hidden, not well-known restrictions operating in the field of natural languages. Most of the restrictions of this type are similar in each natural language. Our direct concern will be the Romanian language.

Selection-for-action emerges in neural networks trained to learn spatial associations between stimuli and actions.

The objects present in our environment evoke multiple conflicting actions at every moment. Thus, a mechanism that resolves this conflict is needed in order to avoid the production of chaotic ineffective behaviours. A plausible candidate for such role is the selective attention, capable of inhibiting the neural representations of the objects irrelevant in the ongoing context and as a consequence the actions they afford. In this paper, we investigated whether a selective attention mechanism emerges spontaneously during the learning of context-dependent behaviour, whereas most neurocomputational models of selective attention and action selection imply the presence of architectural constraints. To this aim, we trained a deep neural network to learn context-dependent visual-action associations. Our main result was the spontaneous emergence of an inhibitory mechanism aimed to solve conflicts between multiple afforded actions by directly suppressing the irrelevant visual stimuli eliciting the incorrect actions for the current context. This suggests that such an inhibitory mechanism emerged as a result of the incorporation of context-independent probabilistic regularities occurring between stimuli and afforded actions.

Examining the influence of working memory on updating mental models.

The ability to accurately build and update mental representations of our environment depends on our ability to integrate information over a variety of time scales and detect changes in the regularity of events. As such, the cognitive mechanisms that support model building and updating are likely to interact with those involved in working memory (WM). To examine this, we performed three experiments that manipulated WM demands concurrently with the need to attend to regularities in other stimulus properties (i.e., location and shape). That is, participants completed a prediction task while simultaneously performing an n-back WM task with either no load or a moderate load. The distribution of target locations (Experiment 1) or shapes (Experiments 2 and 3) included some level of probabilistic regularity, which, unbeknown to participants, changed abruptly within each block. Moderate WM load hampered the ability to benefit from target regularities and to adapt to changes in those regularities (i.e., the prediction task). This was most pronounced when both prediction and WM requirements shared the same target feature. Our results show that representational updating depends on free WM resources in a domain-specific fashion.

Dissociating dynamic probability and predictability in observed actions-an fMRI study.

The present fMRI study investigated whether human observers spontaneously exploit the statistical structure underlying continuous action sequences. In particular, we tested whether two different statistical properties can be distinguished with regard to their neural correlates: an action step's predictability and its probability. To assess these properties we used measures from information theory. Predictability of action steps was operationalized by its inverse, conditional entropy, which combines the number of possible action steps with their respective probabilities. Probability of action steps was assessed using conditional surprisal, which increases with decreasing probability. Participants were trained in an action observation paradigm with video clips showing sequences of 9–33 s length with varying numbers of action steps that were statistically structured according to a Markov chain. Behavioral tests revealed that participants implicitly learned this statistical structure, showing that humans are sensitive toward these probabilistic regularities. Surprisal (lower probability) enhanced the BOLD signal in the anterior intraparietal sulcus. In contrast, high conditional entropy, i.e., low predictability, was correlated with higher activity in dorsomedial prefrontal cortex, orbitofrontal gyrus, and posterior intraparietal sulcus. Furthermore, we found a correlation between the anterior hippocampus' response to conditional entropy with the extent of learning, such that the more participants had learnt the structure, the greater the magnitude of hippocampus activation in response to conditional entropy. Findings show that two aspects of predictions can be dissociated: an action's predictability is reflected in a top-down modulation of attentional focus, evident in increased fronto-parietal activation. In contrast, an action's probability depends on the identity of the stimulus itself, resulting in bottom-up driven processing costs in the parietal cortex.

Caudate Resting Connectivity Predicts Implicit Probabilistic Sequence Learning

Abstract Implicit probabilistic sequence learning (IPSL) involves extracting statistical regularities from sequences of events without awareness, and is thought to underlie learning of language and behavioral repertoires of everyday life. We examined whether resting-state functional connectivity networks of the caudate predicted individual differences in IPSL performance measured on a separate day. Whole-brain connectivity maps of a bilateral dorsal caudate (DC) seed were created for each subject and examined for voxelwise correlations with sequence learning performance, as well as with overall response speed. Higher learning scores (but not overall response speed) were associated with stronger resting-state connectivity between the DC and right medial temporal lobe, as well as with lower resting-state connectivity between the DC and premotor regions involved in motor planning. Thus, how well one learns probabilistic regularities without awareness is predicted by the strength of a striato-cortical network in the resting brain.

Likelihood ratio tests and singularities

Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic subsets of the parameter space. We consider large sample asymptotics for the likelihood ratio test of such hypotheses in models that satisfy standard probabilistic regularity conditions. We show that the assumptions of Chernoff's theorem hold for semi-algebraic sets such that the asymptotics are determined by the tangent cone at the true parameter point. At boundary points or singularities, the tangent cone need not be a linear space and limiting distributions other than chi-square distributions may arise. While boundary points often lead to mixtures of chi-square distributions, singularities give rise to nonstandard limits. We demonstrate that minima of chi-square random variables are important for locally identifiable models, and in a study of the factor analysis model with one factor, we reveal connections to eigenvalues of Wishart matrices.

Developing Language Abilities by a Non-verbal Training : A fMRI Study

AbstractThe language ability is a critical aspect of experimental design in functional imaging studies. Today, it is commonly accepted that the brain structures underlying the language are more distributed than the traditional Broca’s and Wernicke’s areas. Currently, some other areas as the premotor cortex, the supplementary motor area, the cerebellum or subcortical structures, notably, are recognised. However, a lesser studied question is to define if it is possible to observe a reorganisation of the activation observed during language tasks when the subjects have been trained to develop non-verbal abilities. Particularly, Bates and Ellman (1996) claim that probabilistic regularities are the basis of the language acquisition processing.

Language acquisition and statistical learning

Statistical learning is a basic mechanism of information processing in the human brain. The purpose lies in the extraction of probabilistic regularities from the multitude of sensory inputs. Principles of statistical learning contribute significantly to language acquisition and presumably also to language recovery following stroke. The empirical database presented in this manuscript demonstrates that the process of word segmentation, acquisition of a lexicon, and acquisition of simple grammatical rules can be entirely explained through statistical learning. Statistical learning is mediated by changes in synaptic weights in neuronal networks. The concept therefore stands at the transition to molecular biology and pharmacology of the neuronal synapse. It still remains to be shown if all aspects of language acquisition can be explained through statistical learning and which regions of the brain are involved in or capable of statistical learning. Principles of effective language training are obvious already. Most important is the massive, repeated interactive exposure. Conscious processing of the stimulus material may not be essential. The crucial principle is a high cooccurrence of language and corresponding sensory processes. This requires a more intense training frequency than traditional aphasia treatment programs provide.

Probabilistic Regularities in Setup Variations in the Level of a Large Inland Water Body: Case Study of the Caspian Sea

The results of probabilistic analysis of data on setup level variations collected during long-term observations at all gages along the Caspian Sea coast are discussed. A procedure for evaluating low-probability sea level extremes is proposed. Estimates are given for the probabilities of outstanding setups in the Caspian Sea and the Sea of Azov.

Probabilistic regularization in inverse optical imaging.

The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical analysis of the noisy data is presented. Particular emphasis is placed on the question of the positivity constraint, which is incorporated into the probabilistically regularized solution by means of a quadratic programming technique. Numerical examples illustrating the main steps of the algorithm are also given.

Unification of some deterministic and probabilistic methods for the solution of linear inverse problems via the principle of maximum entropy on the mean

This paper deals with the resolution of linear inverse problems. We present a mathematical study of the principle of maximum entropy on the mean (PMEM), and show that it is possible to derive from this principle many deterministic and probabilistic regularization techniques, including the well known Tikhonov method as well as the classical entropy method. In particular, within the deterministic family, full attention is devoted to the regularization principle of WIPE, a methodology recently introduced in radio imaging and optical interferometry. The principle in question is based on the concept of resolution as it is usually introduced in physics. The infinite-dimensional linearly constrained optimization problem underlying the PMEM is solved by means of a dual strategy: recent developments on partially finite convex programming are applied to our specific problem. To illustrate our analysis, we also present a few numerical simulations, in which the regularizer of WIPE is compared with entropy.

Probability and Causality: Why Hume and Indeterminism Don't Mix

A basic assumption of this paper is that things and events have causal capacities: in virtue of the properties they possess, they have the power to bring about other events or states. If you want to bring about a certain outcome, it is a good idea to introduce something with the appropriate capacity. The Humean tradition downplays capacities, and conceives of them as no more than misleading ways of referring to lawlike regularities. We want to reverse this idea: it is better to think of lawlike regularities as misleading ways of referring to the exercise of capacities. If we try to tailor our causal claims to match the regularities we see in nature, we will miss a good deal of the causal structure. Much recent discussion of probabilistic causality may be seen as a neo-Humean attempt to explain probabilistic capacities as, in a way, reducible to probabilistic regularities. Causality is supposed to be a relation between events, a relation which holds in virtue of the empirically distinguishable properties that events have; the relation consists in, or at least is marked by, the regular association of these properties. For Hume the association needed to be universal; nowadays a probabilistic association of the right sort will do. This does not work, we want to argue, and the reason is that the right sort of connections between-capacities and properties do not exist. Capacities are carried by properties. That is, you cannot have the capacity without having one of the right properties. But the same property can carry mixed capacities, and so the true complexity of the situation cannot be revealed by the associations of properties. This is what we hope to show here.

Mind and Chance

Much discussed but still unresolved is whether a subject's internal physical structure is a sufficient condition for his beliefs and desires. The question has sometimes been expressed as a question about microstructurally identical Doppelgänger. Imagine two subjects who are identical right down to the ions traversing the synapses. Their senses are stimulated in all the same ways, their bodies execute the same motions, and identical physical events mediate between the sensory inputs and the behavioral outputs. Must they have the very same beliefs and desires? Let us call the thesis that they must, internalism. The internalist may hold that a physical similarity less complete than this will also guarantee identity in beliefs and desires, but certainly, he holds, perfect identity of internal physical histories will suffice.Internalism will be opposed by those who sense that the nature of mentality is closely tied to the nature of explanation in terms of mental states and that in explaining a subject's behavior we cannot abstract, even in principle, from the character of the environment in which the subject is embedded. This essay offers a partial articulation of this point of view and shows how it conflicts with internalism. A consequence of the view to be described is that our attributions of belief must reflect the probabilistic regularities in the subject's environment. As we shall see, this consequence conflicts with internalism in two ways. The first conflict turns on the fact that there is no limit on the possible variety of such regularities. The second conflict turns on the fact that two subjects might by chance have the same micro-structural history though different probabilistic regularities obtain in their respective environments.