Probabilistic Regularities Research Articles

Symmetry, Invariance, and Imprecise Probability

Abstract It is tempting to think that a process of choosing a point at random from the surface of a sphere can be probabilistically symmetric, in the sense that any two regions of the sphere which differ by a rotation are equally likely to include the chosen point. Isaacs, Hájek and Hawthorne (2022) argue from such symmetry principles and the mathematical paradoxes of measure to the existence of imprecise chances and the rationality of imprecise credences. Williamson (2007) has argued from a related symmetry principle to the failure of probabilistic regularity. We contend that these arguments fail, because they rely on auxiliary assumptions about probability which are inconsistent with symmetry to begin with. We argue, moreover, that symmetry should be rejected in light of this inconsistency, and because it has implausible decision-theoretic implications. The weaker principle of probabilistic invariance says that the probabilistic comparison of any two regions is unchanged by rotations of the sphere. This principle supports a more compelling argument for imprecise probability. We show, however, that invariance is incompatible with mundane judgements about what is probable. Ultimately, we find reason to be suspicious of the application of principles like symmetry and invariance to non-measurable regions.

Twinning quality sensors in wastewater treatment process via optimized echo state network-based soft sensors

The presence of a large amount of quality-related but hard-to-measure variables usually makes effective monitoring of industrial processes difficult, and even impossible. Soft computing techniques and digital twins can revolutionize standard approaches to solve this issue, even though industrial data are frustrated by nonlinearity, disturbances, and dynamic behaviors. In this light, this paper proposes a data-driven soft sensor with the help of the Fourier amplitude sensitivity test (FAST) and improved probabilistic regularized echo state network (IPRESN), then to twin the quality hardware sensors. Within this framework, the initial step is to rely on the FAST method to measure the collaborated importance of multiple process variables with respect to each quality variable. This quantification facilitates the selection of auxiliary variables for the training of IPRESN. Furthermore, a probabilistic regularization method is learned to improve the robust performance of the echo state network (ESN) by re-designing a new objective function to minimize the mean and variance of the modeling error. Additionally, the whale optimization algorithm (WOA) is improved and then used to optimize the critical hyper-parameters of ESN, thus mitigating the risks associated with suboptimal hyperparameter selection. The effectiveness of the proposed method is verified through a Benchmark Simulation Model 2 (BSM2) and a full-scale wastewater treatment plant data set. The findings show the potential of the proposed method in facilitating digital twin implementations for hardware sensors.

Multiscale Coupling and the Maximum of {mathcal {P}}(phi )_2 Models on the Torus

We establish a coupling between the {mathcal {P}}(phi )_2 measure and the Gaussian free field on the two-dimensional unit torus at all spatial scales, quantified by probabilistic regularity estimates on the difference field. Our result includes the well-studied phi ^4_2 measure. The proof uses an exact correspondence between the Polchinski renormalisation group approach, which is used to define the coupling, and the Boué–Dupuis stochastic control representation for {mathcal {P}}(phi )_2. More precisely, we show that the difference field is obtained from a specific minimiser of the variational problem. This allows to transfer regularity estimates for the small-scales of minimisers, obtained using discrete harmonic analysis tools, to the difference field.As an application of the coupling, we prove that the maximum of the {mathcal {P}}(phi )_2 field on the discretised torus with mesh-size epsilon > 0 converges in distribution to a randomly shifted Gumbel distribution as epsilon rightarrow 0.

Handling Ill-conditioned Omics Data with Deep Probabilistic Models.

The advent of high-throughput technologies has produced an increase in the dimensionality of omics datasets, which limits the application of machine learning methods due to the great unbalance between the number of observations and features. In this scenario, dimensionality reduction is essential to extract the relevant information within these datasets and project it in a low-dimensional space, and probabilistic latent space models are becoming popular given their capability to capture the underlying structure of the data as well as the uncertainty in the information. This article aims to provide a general classification and dimensionality reduction method based on deep latent space models that tackles two of the main problems that arise in omics datasets: the presence of missing data and the limited number of observations against the number of features. We propose a semi-supervised Bayesian latent space model that infers a low-dimensional embedding driven by the target label: the Deep Bayesian Logistic Regression (DBLR) model. During inference, the model also learns a global vector of weights that allows it to make predictions given the low-dimensional embedding of the observations. Since this kind of dataset is prone to overfitting, we introduce an additional probabilistic regularization method based on the semi-supervised nature of the model. We compared the performance of the DBLR against several state-of-the-art methods for dimensionality reduction, both in synthetic and real datasets with different data types. The proposed model provides more informative low-dimensional representations, outperforms the baseline methods in classification, and can naturally handle missing entries.

Echo State Network With Probabilistic Regularization for Time Series Prediction

Echo State Network With Probabilistic Regularization for Time Series Prediction

Statistical learning speeds visual search: More efficient selection, or faster response?

Learning statistical regularities of target objects speeds visual search performance. However, we do not yet know whether this statistical learning effect is driven by biasing attentional selection at the early perceptual stage of processing, as theories of attention propose, or by improving the decision-making efficiency at a late response-related stage. Leveraging the high-temporal resolution of the event-related potential (ERP) technique, we had 16 human observers perform a visual search task where we inserted a fine-grained statistical regularity that the target shapes appeared in different colors with six unique probabilities. Observers unintentionally learned these regularities such that they were faster to report targets that appeared in more likely target colors. The observers' ERPs showed that this learning effect resulted in subjects making faster decisions about the target presence, and not by preferentially shifting attention to more rapidly select likely target colors, as is often assumed by the attentional selection account, supporting a post-selection account for statistical learning of the probabilistic regularities of target features. These results provide fundamental insights into the attentional control mechanisms of statistical learning. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Deterministic and probabilistic regularities underlying risky choices are acquired in a changing decision context

Predictions supporting risky decisions could become unreliable when outcome probabilities temporarily change, making adaptation more challenging. Therefore, this study investigated whether sensitivity to the temporal structure in outcome probabilities can develop and remain persistent in a changing decision environment. In a variant of the Balloon Analogue Risk Task with 90 balloons, outcomes (rewards or balloon bursts) were predictable in the task’s first and final 30 balloons and unpredictable in the middle 30 balloons. The temporal regularity underlying the predictable outcomes differed across three experimental conditions. In the deterministic condition, a repeating three-element sequence dictated the maximum number of pumps before a balloon burst. In the probabilistic condition, a single probabilistic regularity ensured that burst probability increased as a function of pumps. In the hybrid condition, a repeating sequence of three different probabilistic regularities increased burst probabilities. In every condition, the regularity was absent in the middle 30 balloons. Participants were not informed about the presence or absence of the regularity. Sensitivity to both the deterministic and hybrid regularities emerged and influenced risk taking. Unpredictable outcomes of the middle phase did not deteriorate this sensitivity. In conclusion, humans can adapt their risky choices in a changing decision environment by exploiting the statistical structure that controls how the environment changes.

A working likelihood approach to support vector regression with a data-driven insensitivity parameter

The insensitivity parameter in support vector regression determines the set of support vectors that greatly impacts the prediction. A data-driven approach is proposed to determine an approximate value for this insensitivity parameter by minimizing a generalized loss function originating from the likelihood principle. This data-driven support vector regression also statistically standardizes samples using the scale of noises different from conventional response scaling method. Statistical standardization together with probabilistic regularization based on a working likelihood function produces data-dependent values for the hyperparameters including the insensitivity parameter. The exact asymptotical solutions are provided when the noises are normally distributed. Nonlinear and linear numerical simulations with three types of noises (epsilon-Laplacian distribution, normal distribution, and uniform distribution), and in addition, five real benchmark data sets, are used to test the capacity of the proposed method. Based on all the simulations and the five case studies, the proposed support vector regression using a working likelihood, data-driven insensitivity parameter is superior and has lower computational costs.

Sustained Pupil Responses Are Modulated by Predictability of Auditory Sequences.

The brain is highly sensitive to auditory regularities and exploits the predictable order of sounds in many situations, from parsing complex auditory scenes, to the acquisition of language. To understand the impact of stimulus predictability on perception, it is important to determine how the detection of predictable structure influences processing and attention. Here, we use pupillometry to gain insight into the effect of sensory regularity on arousal. Pupillometry is a commonly used measure of salience and processing effort, with more perceptually salient or perceptually demanding stimuli consistently associated with larger pupil diameters. In two experiments we tracked human listeners' pupil dynamics while they listened to sequences of 50-ms tone pips of different frequencies. The order of the tone pips was either random, contained deterministic (fully predictable) regularities (experiment 1, n = 18, 11 female) or had a probabilistic regularity structure (experiment 2, n = 20, 17 female). The sequences were rapid, preventing conscious tracking of sequence structure thus allowing us to focus on the automatic extraction of different types of regularities. We hypothesized that if regularity facilitates processing by reducing processing demands, a smaller pupil diameter would be seen in response to regular relative to random patterns. Conversely, if regularity is associated with heightened arousal and attention (i.e., engages processing resources) the opposite pattern would be expected. In both experiments we observed a smaller sustained (tonic) pupil diameter for regular compared with random sequences, consistent with the former hypothesis and confirming that predictability facilitates sequence processing.SIGNIFICANCE STATEMENT The brain is highly sensitive to auditory regularities. To appreciate the impact that the presence of predictability has on perception, we need to better understand how a predictable structure influences processing and attention. We recorded listeners' pupil responses to sequences of tones that followed either a predictable or unpredictable pattern, as the pupil can be used to implicitly tap into these different cognitive processes. We found that the pupil showed a smaller sustained diameter to predictable sequences, indicating that predictability eased processing rather than boosted attention. The findings suggest that the pupil response can be used to study the automatic extraction of regularities, and that the effects are most consistent with predictability helping the listener to efficiently process upcoming sounds.

Determination of Energy and Electric Capacity of On-Board Supercapaci-tor Regenerative Energy Storage

Purpose. Development of a method for determining the main functional parameters of on-board supercapacitor recuperative energy storage based on the asymptotic theory of extreme statistics by Gumbel, taking into account stochastic nature of changes in recuperated voltage and current. Methodology. To achieve this purpose, methods, devices and computer systems for temporary registration of recuperated voltages and currents on operating electric locomotives, methods of the theory of random processes and methods of probabilistic and statistical processing of registrograms of voltages and currents were used. Findings. A computational and experimental method for estimating recuperative energy has been proposed and practically applied. A probabilistic method has been developed for determining the energy and electric capacity of on-board supercapacitor recuperative energy storage units. Numerical probabilistic and statistical calculations of the energy and electric capacity of on-board storage for the VL8 and VL11M6 electric locomotives during their operation in the sections of Prydniprovska railway have been carried out. It was found that the energy and electric capacity of on-board storage devices are distributed according to an exponential law with a clear prevalence of their minimum values and in compliance with direct proportionality between them. Originality. For the first time, an autonomous phase of recuperative braking mode of an electric rolling stock has been developed, which makes it possible to significantly reduce the mass and dimension of a supercapacitor storage. The asymptotic theory of extreme statistics by Gumbel was adapted to the method for calculating energy and electric capacity of an on-board storage device, which made it possible to take into account the influence of stochastic nature of changes in the recuperated voltage and current. The probabilistic influence regularities of the change nature in the recuperation energy on the capacity of on-board storage in the phase of recuperative braking have been established. Further development was obtained by a computational-experimental method for assessing the recuperative energy, based on monitoring and using the time dependences of voltage and current obtained in real modes of recuperative braking. For the first time in electric traction systems, it was proposed to carry out the transition from the recuperative braking mode to the recuperative regeneration mode. Practical value. The developed method and technique based on it make it possible to evaluate functional parameters of on-board storage device of all types of electric rolling stock, considering stochastic nature of recuperated voltages and currents. Numerical-graphic dependences of the energy intensity and capacity of the on-board storage are recommended for predicting and evaluating these parameters for various modes of recuperative braking. Since the task of designing an on-board storage unit (in terms of mass and dimensions) is ambiguous, therefore, in each specific case of the type of electric locomotive and recuperation modes, it must be solved individually, taking into account the probability of the corresponding capacitance values.

Swedish noun-phrase structure in Russian-speaking learners: An explorative study of L1 influence and input-frequency effects

Articles pose a particular challenge to second-language learners whose first language does not have them. Variability in article production in these learners is often explained in terms of first-language influence, but there are also suggestions that frequency-biased regularities in the target language itself might play a role. While most second-language research on articles has focused on English, a language with a relatively simple article system, the present study explores first-language influence and input-frequency effects by focusing on Swedish. Swedish expresses definiteness using a complex noun-phrase structure including several free-standing and bound morphemes, some relatively frequent in input, others less frequent. An oral-production task elicited adjectivally modified and non-modified noun phrases in indefinite and definite contexts from 23 foreign-language learners of Swedish who were native speakers of Russian, an inflectional language without articles. The analysis revealed that the learners were more likely to supply high-frequency morphemes than low-frequency ones. Furthermore, while the learners were equally likely to supply bound and free-standing morphemes, only their suppliance of free-standing morphemes was negatively affected by adjectival modification; their suppliance of bound morphemes was not. While the role of cross-linguistic influence should not be neglected, these findings suggest that probabilistic regularities in the linguistic input are a key factor in second-language acquisition of functional morphology.

Implicit anticipation of probabilistic regularities: Larger CNV emerges for unpredictable events

Anticipation of upcoming events plays a crucial role in automatic behaviors. It is, however, still unclear whether the event-related brain potential (ERP) markers of anticipation could track the implicit acquisition of probabilistic regularities that can be considered as building blocks of automatic behaviors. Therefore, in a four-choice reaction time (RT) task performed by young adults (N = 36), the contingent negative variation (CNV) as an ERP marker of anticipation was measured from the onset of a cue stimulus until the presentation of a target stimulus. Due to the probability structure of the task, target stimuli were either predictable or unpredictable, but this was unknown to participants. The cue did not contain predictive information on the upcoming target. Results showed that the CNV amplitude during response preparation was larger before the unpredictable than before the predictable target stimuli. In addition, although RTs increased, the P3 amplitude decreased for the unpredictable as compared with the predictable target stimuli, possibly due to the stronger response preparation that preceded stimulus presentation. These results suggest that enhanced attentional resources are allocated to the implicit anticipation and processing of unpredictable events. This might originate from the formation of internal models on the probabilistic regularities of the stimulus stream, which primarily facilitates the processing of predictable events. Overall, we provide ERP evidence that supports the role of implicit anticipation and predictive processes in the acquisition of probabilistic regularities.

FUNCTIONAL DIFFERENTIATION OF SPACE AND THE TEN-ELEMENT NUMERICAL MODEL OF ANCIENT CULTURES

The probabilistic regularities in the principles of functional diff erentiation of ordered structures that arise in the process of human space exploration are analyzed. The authors provide the rationale for the ten-element functional model in the context of the wave approach of D.V. Denisov and the fractal-cluster model. Comparable results were obtained for the administrative division into inner-city districts, the structure of tram routes, and the distribution of premises of a Russian university. The analysis is carried out on the example of Samara and Samara State University of Railways.

Potential and efficiency of statistical learning closely intertwined with individuals\u2019 executive functions: a mathematical modeling study

Statistical learning (SL) is essential in enabling humans to extract probabilistic regularities from the world. The ability to accomplish ultimate learning performance with training (i.e., the potential of learning) has been known to be dissociated with performance improvement per amount of learning time (i.e., the efficiency of learning). Here, we quantified the potential and efficiency of SL separately through mathematical modeling and scrutinized how they were affected by various executive functions. Our results showed that a high potential of SL was associated with poor inhibition and good visuo-spatial working memory, whereas high efficiency of SL was closely related to good inhibition and good set-shifting. We unveiled the distinct characteristics of SL in relation to potential and efficiency and their interaction with executive functions.

Global $C^{1}$ regularity of the value function in optimal stopping problems

We show that if either the process is strong Feller and the boundary point is probabilistically regular for the stopping set, or the process is strong Markov and the boundary point is probabilistically regular for the interior of the stopping set, then the boundary point is Green regular for the stopping set. Combining this implication with the existence of a continuously differentiable flow of the process we show that the value function is continuously differentiable at the optimal stopping boundary whenever the gain function is so. The derived fact holds both in the parabolic and elliptic case of the boundary value problem under the sole hypothesis of probabilistic regularity of the optimal stopping boundary, thus improving upon known analytic results in the PDE literature, and establishing the fact for the first time in the case of integro-differential equations. The method of proof is purely probabilistic and conceptually simple. Examples of application include the first known probabilistic proof of the fact that the time derivative of the value function in the American put problem is continuous across the optimal stopping boundary.

Effective noise reduction algorithm for material decomposition in dual-energy X-ray inspection

Dual-energy X-ray inspection can provide material-decomposed transmission information of the imaged object enhancing observer’s inspection performance. The material decomposition algorithms have an inherent noise amplification problem due to the multiplication and division operations during dual-energy image processing, which often degrades the material decomposition performance. In this work, we propose an effective and reliable clustering algorithm to resolve the noise amplification problem. The proposed method utilizes a k-means cluster algorithm as a base method with Gaussian noise of the data considered. In addition, we added a probabilistic regularization that can effectively relieve the decision challenge of the initial number of clusters. We have applied the proposed denoising method to the prototype X-ray dual-energy inspection system with an empirical calibration method that we have previously proposed. The proposed algorithm showed substantial reduction of noise in the test container projections and accordingly improved the material decomposition accuracy. Moreover, we performed quantitative analysis of the empirical calibration method with and without the cluster-based noise reduction algorithm and also on the conventional calibration method for material decomposition. It showed that the empirical calibration method with the noise reduction algorithm is robust against the thickness variation of the target object. The results suggest that the proposed noise reduction algorithm with the empirical calibration method is a promising solution to dual-energy X-ray material decomposition for inspection.

Is there more room to improve? The lifespan trajectory of procedural learning and its relationship to the between- and within-group differences in average response times.

Characterizing the developmental trajectories of cognitive functions such as learning, memory and decision making across the lifespan faces fundamental challenges. Cognitive functions typically encompass several processes that can be differentially affected by age. Methodological issues also arise when comparisons are made across age groups that differ in basic performance measures, such as in average response times (RTs). Here we focus on procedural learning–a fundamental cognitive function that underlies the acquisition of cognitive, social, and motor skills–and demonstrate how disentangling subprocesses of learning and controlling for differences in average RTs can reveal different developmental trajectories across the human lifespan. Two hundred-seventy participants aged between 7 and 85 years performed a probabilistic sequence learning task that enabled us to separately measure two processes of procedural learning, namely general skill learning and statistical learning. Using raw RT measures, in between-group comparisons, we found a U-shaped trajectory with children and older adults exhibiting greater general skill learning compared to adolescents and younger adults. However, when we controlled for differences in average RTs (either by using ratio scores or focusing on a subsample of participants with similar average speed), only children (but not older adults) demonstrated superior general skill learning consistently across analyses. Testing the relationship between average RTs and general skill learning within age groups shed light on further age-related differences, suggesting that general skill learning measures are more affected by average speed in some age groups. Consistent with previous studies of learning probabilistic regularities, statistical learning showed a gradual decline across the lifespan, and learning performance seemed to be independent of average speed, regardless of the age group. Overall, our results suggest that children are superior learners in various aspects of procedural learning, including both general skill and statistical learning. Our study also highlights the importance to test, and control for, the effect of average speed on other RT measures of cognitive functions, which can fundamentally affect the interpretation of group differences in developmental, aging and clinical psychology and neuroscience studies.

Comparing statistical learning across perceptual modalities in infancy: An investigation of underlying learning mechanism(s).

Statistical learning (SL), sensitivity to probabilistic regularities in sensory input, has been widely implicated in cognitive and perceptual development. Little is known, however, about the underlying mechanisms of SL and whether they undergo developmental change. One way to approach these questions is to compare SL across perceptual modalities. While a decade of research has compared auditory and visual SL in adults, we present the first direct comparison of visual and auditory SL in infants (8-10months). Learning was evidenced in both perceptual modalities but with opposite directions of preference: Infants in the auditory condition displayed a novelty preference, while infants in the visual condition showed a familiarity preference. Interpreting these results within the Hunter and Ames model (1988), where familiarity preferences reflect a weaker stage of encoding than novelty preferences, we conclude that there is weaker learning in the visual modality than the auditory modality for this age. In addition, we found evidence of different developmental trajectories across modalities: Auditory SL increased while visual SL did not change for this age range. The results suggest that SL is not an abstract, amodal ability; for the types of stimuli and statistics tested, we find that auditory SL precedes the development of visual SL and is consistent with recent work comparing SL across modalities in older children.

Tracking the implicit acquisition of nonadjacent transitional probabilities by ERPs

The implicit acquisition of complex probabilistic regularities has been found to be crucial in numerous automatized cognitive abilities, including language processing and associative learning. However, it has not been completely elucidated how the implicit extraction of second-order nonadjacent transitional probabilities is reflected by neurophysiological processes. Therefore, this study investigated the sensitivity of event-related brain potentials (ERPs) to these probabilistic regularities embedded in a sequence of visual stimuli without providing explicit information on the structure of the stimulus stream. Healthy young adults (N = 32) performed a four-choice RT task that included a sequential regularity between nonadjacent trials yielding a complex transitional probability structure. ERPs were measured relative to both stimulus and response onset. RTs indicated the rapid acquisition of the sequential regularity and the transitional probabilities. The acquisition process was also tracked by the stimulus-locked and response-locked P3 component: The P3 peak was larger for the sequence than for the random stimuli, while the late P3 was larger for less probable than for more probable short-range relations among the random stimuli. According to the RT and P3 effects, sensitivity to the sequential regularity is assumed to be supported by the initial sensitivity to the transitional probabilities. These results suggest that stimulus–response contingencies on the probabilistic regularities of the ongoing stimulus context are implicitly mapped and constantly revised. Overall, this study (1) highlights the role of predictive processes during implicit memory formation, and (2) delineates a potential to gain further insight into the dynamics of implicit acquisition processes.

Traces of statistical learning in the brain's functional connectivity after artificial language exposure

Our environment is full of statistical regularities, and we are attuned to learn about these regularities by employing Statistical Learning (SL), a domain-general ability that enables the implicit detection of probabilistic regularities in our surrounding environment. The role of brain connectivity on SL has been previously explored, highlighting the relevance of structural and functional connections between frontal, parietal, and temporal cortices. However, whether SL can induce changes in the functional connections of the resting state brain has yet to be investigated. To address this question, we applied a pre-post design where participants (n = 38) were submitted to resting-state fMRI acquisition before and after in-scanner exposure to either an artificial language stream (formed by 4 concatenated words) or a random audio stream. Our results showed that exposure to an artificial language stream significantly changed (corrected p < 0.05) the functional connectivity between Right Posterior Cingulum and Left Superior Parietal Lobule. This suggests that functional connectivity between brain networks supporting attentional and working memory processes may play an important role in statistical learning.