Tracking probabilistic truths: a logic for statistical learning

AbstractWe propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent’s beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds (or more generally, truth in all the worlds that are plausible enough). We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: (1) learning observable evidence obtained by repeated sampling from the unknown distribution; and (2) learning higher-order information about the distribution. The first changes only the plausibility map (via a ‘plausibilistic’ version of Bayes’ Rule), but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions (safe belief and statistical knowledge), as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent’s beliefs track the true probability after repeated sampling, and how she eventually gains in a sense (statistical) knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning.

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Review of Statistical Learning Methods in Integrated Omics Studies (An Integrated Information Science)

Bioinformatics and Biology Insights ◽

10.1177/1177932218759292 ◽

2018 ◽

Vol 12 ◽

pp. 117793221875929 ◽

Cited By ~ 23

Author(s):

Irene Sui Lan Zeng ◽

Thomas Lumley

Keyword(s):

Machine Learning ◽

Statistical Learning ◽

Information Science ◽

Molecular System ◽

Principal Component ◽

Statistical Machine Learning ◽

Learning Methods ◽

Integrated Omics ◽

Types Of Information ◽

Integrated Information

Integrated omics is becoming a new channel for investigating the complex molecular system in modern biological science and sets a foundation for systematic learning for precision medicine. The statistical/machine learning methods that have emerged in the past decade for integrated omics are not only innovative but also multidisciplinary with integrated knowledge in biology, medicine, statistics, machine learning, and artificial intelligence. Here, we review the nontrivial classes of learning methods from the statistical aspects and streamline these learning methods within the statistical learning framework. The intriguing findings from the review are that the methods used are generalizable to other disciplines with complex systematic structure, and the integrated omics is part of an integrated information science which has collated and integrated different types of information for inferences and decision making. We review the statistical learning methods of exploratory and supervised learning from 42 publications. We also discuss the strengths and limitations of the extended principal component analysis, cluster analysis, network analysis, and regression methods. Statistical techniques such as penalization for sparsity induction when there are fewer observations than the number of features and using Bayesian approach when there are prior knowledge to be integrated are also included in the commentary. For the completeness of the review, a table of currently available software and packages from 23 publications for omics are summarized in the appendix.

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Statistical Properties in Jazz Improvisation Underline Individuality of Musical Representation

NeuroSci ◽

10.3390/neurosci1010004 ◽

2020 ◽

Vol 1 (1) ◽

pp. 24-43

Author(s):

Tatsuya Daikoku

Keyword(s):

Statistical Learning ◽

Time Course ◽

Statistical Properties ◽

Transitional Probability ◽

Jazz Improvisation ◽

Statistical Knowledge ◽

Future State ◽

Structured Information ◽

Transitional Probabilities ◽

The Brain

Statistical learning is an innate function in the brain and considered to be essential for producing and comprehending structured information such as music. Within the framework of statistical learning the brain has an ability to calculate the transitional probabilities of sequences such as speech and music, and to predict a future state using learned statistics. This paper computationally examines whether and how statistical learning and knowledge partially contributes to musical representation in jazz improvisation. The results represent the time-course variations in a musician’s statistical knowledge. Furthermore, the findings show that improvisational musical representation might be susceptible to higher- but not lower-order statistical knowledge (i.e., knowledge of higher-order transitional probability). The evidence also demonstrates the individuality of improvisation for each improviser, which in part depends on statistical knowledge. Thus, this study suggests that statistical properties in jazz improvisation underline individuality of musical representation.

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Neurophysiological coding of statistical and deterministic rule information

10.1101/2020.10.14.338913 ◽

2020 ◽

Author(s):

Ádám Takács ◽

Andrea Kóbor ◽

Zsófia Kardos ◽

Karolina Janacsek ◽

Kata Horváth ◽

...

Keyword(s):

Statistical Learning ◽

Visual Information ◽

Time Window ◽

Learning Mechanisms ◽

Decomposition Approach ◽

Rule Based ◽

Parallel Learning ◽

Time Sensitivity ◽

Types Of Information ◽

The Right

AbstractHumans are capable of acquiring multiple types of information presented in the same visual information stream. It has been suggested that at least two parallel learning processes are important during learning of sequential patterns – statistical learning and rule-based learning. Yet, the neurophysiological underpinnings of these parallel learning mechanisms in visual sequences are not fully understood. To differentiate between the simultaneous mechanisms at the single trial level, we apply a temporal EEG signal decomposition approach together with sLORETA source localization method to delineate whether distinct statistical and rule-based learning codes can be distinguished in EEG data and can be related to distinct functional neuroanatomical structures. We demonstrate that concomitant but distinct aspects of information coded in the N2 time window play a role in these mechanisms: mismatch detection and response control underlie statistical learning and rule-based learning, respectively, albeit with different levels of time-sensitivity. Moreover, the effects of the two learning mechanisms in the different temporally decomposed clusters of neural activity also differed from each other in neural sources. Importantly, the right inferior frontal cortex (BA44) was specifically implicated in statistical learning, confirming its role in the acquisition of transitional probabilities. In contrast, rule-based learning was associated with the prefrontal gyrus (BA6). The results show how simultaneous learning mechanisms operate at the neurophysiological level and are orchestrated by distinct prefrontal cortical areas. The current findings deepen our understanding on the mechanisms how humans are capable of learning multiple types of information from the same stimulus stream in a parallel fashion.

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Improved Regularization Method for Backward Cauchy Problems Associated with Continuous Spectrum Operator

International Journal of Differential Equations ◽

10.1155/2011/913125 ◽

2011 ◽

Vol 2011 ◽

pp. 1-11

Author(s):

Salah Djezzar ◽

Nihed Teniou

Keyword(s):

Continuous Spectrum ◽

Original Problem ◽

Convergence Rates ◽

Nonlocal Problem ◽

Cauchy Problems ◽

Final Time ◽

Unbounded Linear Operator ◽

Convergence Results ◽

Small Parameters ◽

The Given

We consider in this paper an abstract parabolic backward Cauchy problem associated with an unbounded linear operator in a Hilbert space , where the coefficient operator in the equation is an unbounded self-adjoint positive operator which has a continuous spectrum and the data is given at the final time and a solution for is sought. It is well known that this problem is illposed in the sense that the solution (if it exists) does not depend continuously on the given data. The method of regularization used here consists of perturbing both the equation and the final condition to obtain an approximate nonlocal problem depending on two small parameters. We give some estimates for the solution of the regularized problem, and we also show that the modified problem is stable and its solution is an approximation of the exact solution of the original problem. Finally, some other convergence results including some explicit convergence rates are also provided.

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Two categorization patterns in idiom semantics

Pragmatics & Cognition ◽

10.1075/pc.23.2.08gor ◽

2016 ◽

Vol 23 (2) ◽

pp. 343-358 ◽

Cited By ~ 1

Author(s):

Chermen Gogichev

Keyword(s):

Cognitive Processes ◽

Cognitive Functions ◽

Linguistic Analysis ◽

Interaction Models ◽

Effect Relationship ◽

Semantic Organization ◽

Behavioral Expectations ◽

Different Types ◽

Types Of Information ◽

The Given

The article looks at idioms as categorization means. On the basis of linguistic analysis of semantic organization of idioms two patterns of idiomatic categorization are argued — general categorization and relevant property based categorization. Cognitive functions of idioms differ with regard to their role as categorization means, idioms can serve different categorization purposes according to two general cognitive processes — static and dynamic — including in a category or considering the given qualities as the reasons for categorization. Moreover, the purpose of categorization was investigated with defining the specificity of the phenomena and its types. The categorization purpose was conceived as different types of information e.g. behavioral expectations or interaction models with the object. The cause-effect relationship between the category and the categorization purpose was claimed.

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PEMBELAJARAN STATISTIKA DALAM PERSPEKTIF GENDER

Tarbawiyah Jurnal Ilmiah Pendidikan ◽

10.32332/tarbawiyah.v2i02.1415 ◽

2018 ◽

Vol 2 (02) ◽

pp. 282

Author(s):

Yuyun Yunarti

Keyword(s):

Gender Differences ◽

Statistical Learning ◽

Female Students ◽

The Other ◽

Daily Lives ◽

Men And Women ◽

Statistical Knowledge ◽

Other Hand ◽

Gender Aspects

Statistics is considered a boring subject for students, even though statistics are taught with the aim of preparing students to be able to use statistics in their daily lives. In studying statistics, there are still many students both men and women who view statistics as a boring subject. Based on this, the gender aspects of statistical learning are of concern to educators. Gender differences not only result in differences in abilities in statistical courses, but also in obtaining statistical knowledge. Many opinions say that women are not enough to successfully study statistics compared to men. In addition, women almost never have a thorough interest in theoretical questions like men. Women are more interested in practical things than theoretical ones. But on the other hand, not a few female students have success in statistical abilities.

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Identification information sensors of robot systems

Indonesian Journal of Electrical Engineering and Computer Science ◽

10.11591/ijeecs.v14.i3.pp1235-1243 ◽

2019 ◽

Vol 14 (3) ◽

pp. 1235

Author(s):

Igor Parkhomey ◽

Juliy Boiko ◽

Oleksander Eromenko

Keyword(s):

Decision Rule ◽

Autocorrelation Function ◽

Optimal Decision ◽

Bayes Rule ◽

Optimal Decision Rule ◽

Invariant Description ◽

Robot Systems ◽

Similarity Class ◽

Definition Of ◽

The Given

At the present time, the complexity of identification is to find such a description, in which the image (information) of each class would have identified similar properties. The task is to make the transformed description includes the whole set of input images, united by the similarity class by the given ratio.Using the ordinates of an autocorrelation function is an inseparable shift in the center of gravity of an image, which leads to a change of such description.Nicest, the concept of an invariant description of information arises, this is an autocorrelation function, which is invariant to the description of any displacements of the image in the vertical and horizontal directions.The problem of finding an optimal decision rule arises, which, in a number of cases, can be constructed on the basis of a method, based on the definition of the maximum incomplete coefficient of similarity.Using this method, the solutions, that are almost unintelligible to the errors that arise due to the effects of interference, are found. Therefore, in increments k, this rule passes into the Bayes’ rule.

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Is infant-directed speech interesting because it is surprising? – Linking properties of IDS to statistical learning and attention at the prosodic level

10.31234/osf.io/um6d7 ◽

2017 ◽

Author(s):

Okko Räsänen ◽

Sofoklis Kakouros ◽

Melanie Soderstrom

Keyword(s):

Statistical Learning ◽

Information Value ◽

Attentional Processing ◽

Young Infants ◽

Linguistic Patterns ◽

Temporal Predictability ◽

Pitch Contours ◽

The Difference ◽

Short Utterances ◽

The Given

The exaggerated intonation and special rhythmic properties of infant-directed speech (IDS) have been hypothesized to attract infant’s attention to the speech stream. However, there has been little work actually connecting the properties of IDS to models of attentional processing or perceptual learning. A number of such attention models suggest that surprising or novel perceptual inputs attract attention, where novelty can be operationalized as the statistical (un)predictability of the stimulus in the given context. Since prosodic patterns such as F0 contours are accessible to young infants who are also known to be adept statistical learners, the present paper investigates a hypothesis that F0 contours in IDS are less predictable than those in adult-directed speech (ADS), given previous exposure to both speaking styles, thereby potentially tapping into basic attentional mechanisms of the listeners in a similar manner that relative probabilities of other linguistic patterns are known to modulate attentional processing in infants and adults. Computational modeling analyses with naturalistic IDS and ADS speech from matched speakers and contexts show that IDS intonation has lower overall temporal predictability even when the F0 contours of both speaking styles are normalized to have equal means and variances. A closer analysis reveals that there is a tendency of IDS intonation to be less predictable at the end of short utterances whereas ADS exhibits more stable average predictability patterns across the full extent of the utterances. The difference between IDS and ADS persists even when the proportion of IDS and ADS exposure is varied substantially, simulating different relative amounts of IDS heard in different family and cultural environments. Exposure to IDS is also found to be more efficient for predicting ADS pitch contours in new utterances than exposure to the equal amount of ADS speech, indicating that the more variable prosodic contours of IDS also generalize to ADS, and may therefore enhance prosodic learning in infancy. Overall, the study suggests that one reason behind infant preference for IDS could be its higher information value at the prosodic level, as measured by the amount of surprisal in the F0 contours, providing the first formal link between the properties of IDS and the models of attentional processing and statistical learning in the brain. However, this finding does not rule out the possibility that other differences between the IDS and ADS also play a role.

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Divided attention does not affect the acquisition and consolidation of transitional probabilities

Scientific Reports ◽

10.1038/s41598-020-79232-y ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Kata Horváth ◽

Csenge Török ◽

Orsolya Pesthy ◽

Dezso Nemeth ◽

Karolina Janacsek

Keyword(s):

Statistical Learning ◽

Divided Attention ◽

Reaction Time Task ◽

Learning Task ◽

Second Order ◽

The Other ◽

Attentional Processes ◽

Statistical Knowledge ◽

Environmental Events ◽

Transitional Probabilities

AbstractStatistical learning facilitates the efficient processing and prediction of environmental events and contributes to the acquisition of automatic behaviors. Whereas a minimal level of attention seems to be required for learning to occur, it is still unclear how acquisition and consolidation of statistical knowledge are affected when attention is divided during learning. To test the effect of divided attention on statistical learning and consolidation, ninety-six healthy young adults performed the Alternating Serial Reaction Time task in which they incidentally acquired second-order transitional probabilities. Half of the participants completed the task with a concurrent secondary intentional sequence learning task that was applied to the same stimulus stream. The other half of the participants performed the task without any attention manipulation. Performance was retested after a 12-h post-learning offline period. Half of each group slept during the delay, while the other half had normal daily activity, enabling us to test the effect of delay activity (sleep vs. wake) on the consolidation of statistical knowledge. Divided attention had no effect on statistical learning: The acquisition of second-order transitional probabilities was comparable with and without the secondary task. Consolidation was neither affected by divided attention: Statistical knowledge was similarly retained over the 12-h delay, irrespective of the delay activity. Our findings can contribute to a better understanding of the role of attentional processes in and the robustness of visuomotor statistical learning and consolidation.

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Chebyshev-Fourier Spectral Methods for Nonperiodic Boundary Value Problems

Journal of Applied Mathematics ◽

10.1155/2014/572694 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Bojan Orel ◽

Andrej Perne

Keyword(s):

Numerical Solution ◽

Boundary Value Problems ◽

Spectral Methods ◽

Boundary Value ◽

Absolute Error ◽

Method Error ◽

Linear Ordinary Differential Equations ◽

New Class ◽

Convergence Results ◽

The Given

A new class of spectral methods for solving two-point boundary value problems for linear ordinary differential equations is presented in the paper. Although these methods are based on trigonometric functions, they can be used for solving periodic as well as nonperiodic problems. Instead of using basis functions periodic on a given interval−1,1, we use functions periodic on a wider interval. The numerical solution of the given problem is sought in terms of the half-range Chebyshev-Fourier (HCF) series, a reorganization of the classical Fourier series using half-range Chebyshev polynomials of the first and second kind which were first introduced by Huybrechs (2010) and further analyzed by Orel and Perne (2012). The numerical solution is constructed as a HCF series via differentiation and multiplication matrices. Moreover, the construction of the method, error analysis, convergence results, and some numerical examples are presented in the paper. The decay of the maximal absolute error according to the truncation numberNfor the new class of Chebyshev-Fourier-collocation (CFC) methods is compared to the decay of the error for the standard class of Chebyshev-collocation (CC) methods.

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