We introduce martingales defined by probabilistic strategies, in which randomness is used to decide whether to bet. We show that different criteria for the success of computable probabilistic strategies can be used to characterize ML-randomness, computable randomness, and partial computable randomness. Our characterization of ML-randomness partially addresses a critique of Schnorr by formulating ML randomness in terms of a computable process rather than a computably enumerable function.

We consider two ways one might use algorithmic randomness to characterize a probabilistic law. The first is a generative chance* law. Such laws involve a nonstandard notion of chance. The second is a probabilistic* constraining law. Such laws impose relative frequency and randomness constraints that every physically possible world must satisfy. While each notion has virtues, we argue that the latter has advantages over the former. It supports a unified governing account of non-Humean laws and provides independently motivated (...) solutions to issues in the Humean best-system account. On both notions, we have a much tighter connection between probabilistic laws and their corresponding sets of possible worlds. Certain histories permitted by traditional probabilistic laws are ruled out as physically impossible. As a result, such laws avoid one variety of empirical underdetermination, but the approach reveals other varieties of underdetermination that are typically overlooked. (shrink)

PROBEX (PROBabilities from EXemplars), a model of probabilistic inference and probability judgment based on generic knowledge is presented. Its properties are that: (a) it provides an exemplar model satisfying bounded rationality; (b) it is a “lazy” algorithm that presumes no pre‐computed abstractions; (c) it implements a hybrid‐representation, similarity‐graded probability. We investigate the ecological rationality of PROBEX and find that it compares favorably with Take‐The‐Best and multiple regression (Gigerenzer, Todd, & the ABC Research Group, 1999). PROBEX is fitted to the (...) point estimates, decisions, and probability assessments by human participants. The best fit is obtained for a version that weights frequency heavily and retrieves only two exemplars. It is proposed that PROBEX implements speed and frugality in a psychologically plausible way. (shrink)

In many real-life situations, we are interested in the value of a physical quantity y that is difficult or impossible to measure directly. To estimate y, we find some easier-to-measure quantities x1, … , xn which are related to y by a known relation y = f. Measurements are never 100% accurate; hence, the measured values equation image are different from xi, and the resulting estimate equation image is different from the desired value y = f. How different can it (...) be? Traditional engineering approach to error estimation in data processing assumes that we know the probabilities of different measurement errors equation image. In many practical situations, we only know the upper bound Δi for this error; hence, after the measurement, the only information that we have about xi is that it belongs to the interval equation image. In this case, it is important to find the range y of all possible values of y = f when xi ∈ xi. We start the paper with a brief overview of the computational complexity of the corresponding interval computation problems: Most of the related problems turn out to be, in general, at least NP-hard. In this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether “hypothetic” physical devices can compute NP-hard problems faster than in exponential time. Most of the paper's results were first presented at NAFIPS'2003 [30]. (shrink)

The problems of access—retrieving linguistic structure from some mental grammar —and disambiguation—choosing among these structures to correctly parse ambiguous linguistic input—are fundamental to language understanding. The literature abounds with psychological results on lexical access, the access of idioms, syntactic rule access, parsing preferences, syntactic disambiguation, and the processing of garden‐path sentences. Unfortunately, it has been difficult to combine models which account for these results to build a general, uniform model of access and disambiguation at the lexical, idiomatic, and syntactic levels. (...) For example, psycholinguistic theories of lexical access and idiom access and parsing theories of syntactic rule access have almost no commonality in methodology or coverage of psycholinguistic data. This article presents a single probabilistic algorithm which models both the access and disambiguation of linguistic knowledge. The algorithm is based on a parallel parser which ranks constructions for access, and interpretations for disambiguation, by their conditional probability. Low‐ranked constructions and interpretations are pruned through beam‐search; this pruning accounts, among other things, for the garden‐path effect. I show that this motivated probabilistic treatment accounts for a wide variety of psycholinguistic results, arguing for a more uniform representation of linguistic knowledge and for the use of probabilistically‐enriched grammars and interpreters as models of human knowledge of and processing of language. (shrink)

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model- theoretic probabilistic reasoning and to default reasoning in System . In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization (...) of default reasoning in System . That is, we provide a new probabilistic semantics for System , which neither uses infinitesimal probabilities nor atomic bound (or big-stepped) probabilities. These results also provide new algorithms for probabilistic reasoning under coherence and for default reasoning in System , and they give new insight into default reasoning with conditional objects. (shrink)

Estimation of Distribution Algorithms, which employ probabilistic models to generate the next population, are new promising methods in the field of genetic and evolutionary algorithms. In the case of conventional Genetic and Evolutionary Algorithms are applied to Constraint Satisfaction Problems, it is well-known that the incorporation of the domain knowledge in the Constraint Satisfaction Problems is quite effective. In this paper, we constitute a memetic algorithm as a combination of the Estimation of Distribution Algorithm and a (...) repair method. Experimental results on general Constraint Satisfaction Problems tell us the effectiveness of the proposed method. (shrink)

This book is the result of several decades of teaching experience in data structures and algorithms. It is self-contained but does assume some prior knowledge of data structures, and a grasp of basic programming and mathematics tools. Basic Concepts in Algorithms focuses on more advanced paradigms and methods combining basic programming constructs as building blocks and their usefulness in the derivation of algorithms. Its coverage includes the algorithms' design process and an analysis of their performance. It (...) is primarily intended as a textbook for the teaching of Algorithms for second-year undergraduate students in study fields related to computers and programming. Klein reproduces his oral teaching style in writing, with one topic leading to another, related one. Most of the classical and some more advanced subjects in the theory of algorithms are covered, though not in a comprehensive manner. The topics include Divide and Conquer, Dynamic Programming, Graph algorithms, probabilistic algorithms, data compression, numerical algorithms and intractability. Each chapter comes with its own set of exercises, and solutions to most of them are appended. (shrink)

It seems to be generally accepted that (a) counterfactual conditionals are to be analysed in terms of possible worlds and inter-world relations of similarity and (b) causation is conceptually prior to counterfactuals. I argue here that both (a) and (b) are false. The argument against (a) is not a general metaphysical or epistemological one but simply that, structurally speaking, possible worlds theories are wrong: this is revealed when we try to extend them to cover the case of probabilistic counterfactuals. (...) Indeed a type of counterfactual probability exists which cannot be expressed in possible worlds terms at all. The argument against (b) emerges when we look at the form of an adequate account of both probabilistic and non-probabilistic counterfactuals. I do this by sketching and defending an approach to counterfactuals that, first, invoke a generalized notion of cause as primitive and, secondly, is algorithmic in form: counterfactuals are evaluated algorithmically in terms of other counterfactuals, without vicious circularity. Structures like possible worlds do not play a role either in general truth-conditions or in evaluation. They are simply the wrong sorts of structures. (shrink)

The rapidly increasing role of automation throughout the economy, culture and our personal lives has generated a large literature on the risks of algorithmic decision-making, particularly in high-stakes legal settings. Algorithmic tools are charged with bias, shrouded in secrecy, and frequently difficult to interpret. However, these criticisms have tended to focus on particular implementations, specific predictive techniques, and the idiosyncrasies of the American legal-regulatory regime. They do not address the more fundamental unease about the prospect that we might one day (...) replace judges with algorithms, no matter how fair, transparent, and intelligible they become. The aim of this paper is to propose an account of the source of that unease, and to evaluate its plausibility. I trace foundational unease with algorithmic decision-making in the law to the powerful intuition that there is a basic moral and legal difference between showing that something is true of many people just like you and showing that it is true of you. Human judgment attends to the exception; automation insists on blindly applying the rule. I show how this intuitive thought is connected to both epistemological arguments about the value of statistical evidence, as well as to court-centered conceptions of the rule of law. Unease with algorithmic decision-making in the law thus draws on an intuitive principle that underpins a disparate range of views in legal philosophy. This suggests the principle is deeply ingrained. Nonetheless, I argue that the powerful intuition is not as decisive as it may seem, and indeed runs into significant epistemological and normative challenges. At an epistemological level, I show how concerns about statistical evidence's ability to track the truth can be resolved by adopting a probabilistic, rather than modal, conception of truth-tracking. At a normative level, commitment to highly individualized decision-making co-exists with equally ingrained and competing principles, such as consistent application of law. This suggests that the “rule of law” may not identify a discrete set of institutional arrangements, as proponents of a court-centric conception would have it, but rather a more loosely defined set of values that could potentially be operationalized in multiple ways, including through some level of algorithmic adjudication. Although the prospect of replacing judges with algorithms is indeed unsettling, it does not necessarily entail unreasonable verdicts or an attack on the rule of law. (shrink)

A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, (...) and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals. (shrink)

We study the existence of efficient approximation methods to verify quantitative specifications of probabilistic systems. Models of such systems are labelled discrete time Markov chains and checking specifications consists of computing satisfaction probabilities of linear temporal logic formulas. We prove that, in general, there is no polynomial time randomized approximation scheme with relative error for probabilistic verification. However, in many applications, specifications can be expressed by monotone formulas or negation of monotone formulas and randomized approximation schemes with absolute (...) error are sufficient. We show how some simple randomized approximation algorithms can improve the efficiency of verification of such probabilistic specifications and can be implemented in a probabilistic model checker. (shrink)

We present a probabilistic extension to active path analyses of token causation (Halpern & Pearl 2001, forthcoming; Hitchcock 2001). The extension uses the generalized notion of intervention presented in (Korb et al. 2004): we allow an intervention to set any probability distribution over the intervention variables, not just a single value. The resulting account can handle a wide range of examples. We do not claim the account is complete --- only that it fills an obvious gap in previous active-path (...) approaches. It still succumbs to recent counterexamples by Hiddleston (2005), because it does not explicitly consider causal processes. We claim three benefits: a detailed comparison of three active-path approaches, a probabilistic extension for each, and an algorithmic formulation. (shrink)

I discuss the epistemic status of algorithmic predictions in the legal realm. My main claim is that algorithmic predictions do not give us knowledge, not even probabilistic knowledge. The situation, however, is relevantly different from the one in which we find ourselves at the time of assessing statistical evidence in general, and it is rather related to the fact that algorithmic fairness in legal contexts is essentially undetermined. In the light of this, we have to settle for justified beliefs (...) and justified credences. I end by drawing some morals for the Knowledge Norm of action. (shrink)

The sampling-based motion planner is the mainstream method to solve the motion planning problem in high-dimensional space. In the process of exploring robot configuration space, this type of algorithm needs to perform collision query on a large number of samples, which greatly limits their planning efficiency. Therefore, this paper uses machine learning methods to establish a probabilistic model of the obstacle region in configuration space by learning a large number of labeled samples. Based on this, the high-dimensional samples’ rapid (...) collision query is realized. The influence of number of Gaussian components on the fitting accuracy is analyzed in detail, and a self-adaptive model training method based on Greedy expectation-maximization algorithm is proposed. At the same time, this method has the capability of online updating and can eliminate model fitting errors due to environmental changes. Finally, the model is combined with a variety of sampling-based motion planners and is validated in multiple sets of simulations and real world experiments. The results show that, compared with traditional methods, the proposed method has significantly improved the planning efficiency. (shrink)

An unknown process is generating a sequence of symbols, drawn from an alphabet, A. Given an initial segment of the sequence, how can one predict the next symbol? Ray Solomonoff’s theory of inductive reasoning rests on the idea that a useful estimate of a sequence’s true probability of being outputted by the unknown process is provided by its algorithmic probability (its probability of being outputted by a species of probabilistic Turing machine). However algorithmic probability is a “semimeasure”: i.e., the (...) sum, over all x∈A, of the conditional algorithmic probabilities of the next symbol being x, may be less than 1. Prevailing wisdom has it that algorithmic probability must be normalized, to eradicate this semimeasure property, before it can yield acceptable probability estimates. This paper argues, to the contrary, that the semimeasure property contributes substantially to the power and scope of an algorithmic-probability-based theory of induction, and that normalization is unnecessary. (shrink)

Measures of algorithmic bias can be roughly classified into four categories, distinguished by the conditional probabilistic dependencies to which they are sensitive. First, measures of "procedural bias" diagnose bias when the score returned by an algorithm is probabilistically dependent on a sensitive class variable (e.g. race or sex). Second, measures of "outcome bias" capture probabilistic dependence between class variables and the outcome for each subject (e.g. parole granted or loan denied). Third, measures of "behavior-relative error bias" capture (...) class='Hi'>probabilistic dependence between class variables and the algorithmic score, conditional on target behaviors (e.g. recidivism or loan default). Fourth, measures of "score-relative error bias" capture probabilistic dependence between class variables and behavior, conditional on score. Several recent discussions have demonstrated a tradeoff between these different measures of algorithmic bias, and at least one recent paper has suggested conditions under which tradeoffs may be minimized. -/- In this paper we use the machinery of causal graphical models to show that, under standard assumptions, the underlying causal relations among variables forces some tradeoffs. We delineate a number of normative considerations that are encoded in different measures of bias, with reference to the philosophical literature on the wrongfulness of disparate treatment and disparate impact. While both kinds of error bias are nominally motivated by concern to avoid disparate impact, we argue that consideration of causal structures shows that these measures are better understood as complicated and unreliable measures of procedural biases (i.e. disparate treatment). Moreover, while procedural bias is indicative of disparate treatment, we show that the measure of procedural bias one ought to adopt is dependent on the account of the wrongfulness of disparate treatment one endorses. Finally, given that neither score-relative nor behavior-relative measures of error bias capture the relevant normative considerations, we suggest that error bias proper is best measured by score-based measures of accuracy, such as the Brier score. (shrink)

Stochastic forecasts in complex environments can benefit from combining the estimates of large groups of forecasters (“judges”). But aggregating multiple opinions faces several challenges. First, human judges are notoriously incoherent when their forecasts involve logically complex events. Second, individual judges may have specialized knowledge, so different judges may produce forecasts for different events. Third, the credibility of individual judges might vary, and one would like to pay greater attention to more trustworthy forecasts. These considerations limit the value of simple aggregation (...) methods like linear averaging. In this paper, a new algorithm is proposed for combining probabilistic assessments from a large pool of judges. Two measures of a judge’s likely credibility are introduced and used in the algorithm to determine the judge’s weight in aggregation. The algorithm was tested on a data set of nearly half a million probability estimates of events related to the 2008 U.S. presidential election (∼ 16000 judges). (shrink)

Recently, certain philosophers of mathematics (Fallis [1997]; Womack and Farach [(1997]) have argued that there are no epistemic considerations that should stop mathematicians from using probabilistic methods to establish that mathematical propositions are true. However, mathematicians clearly should not use methods that are unreliable. Unfortunately, due to the fact that randomized algorithms are not really random in practice, there is reason to doubt their reliability. In this paper, I analyze the prospects for establishing that randomized algorithms are (...) reliable. I end by arguing that it would be inconsistent for mathematicians to suspend judgement on the truth of mathematical propositions on the basis of worries about the reliability of randomized algorithms. (shrink)

It can be challenging to learn algorithms due to the research of business-related few-shot classification problems. Therefore, in this paper, we evaluate the classification of few-shot learning in the commercial field. To accurately identify the categories of few-shot learning problems, we proposed a probabilistic network method based on few-shot and one-shot learning problems. The enhancement of the original data was followed by the subsequent development of the PN method based on feature extraction, category comparison, and loss function analysis. (...) The effectiveness of the method was validated using two examples. Experimental results demonstrate the ability of the PN method to effectively identify the categories of commercial few-shot learning problems. Therefore, the proposed method can be applied to business-related few-shot classification problems. (shrink)

There is a well-documented paradigm-shift in eighteenth century Jesuit philosophy and science, at the very least in Central Europe: traditional scholastic version(s) of Aristotelianism were replaced by early modern rationalism (Wolff's systematisation of Leibnizian philosophy) and early modern science and mathematics. In the field of probability, this meant that the traditional Jesuit engagement with probability, uncertainty, and truthlikeness (in particular, as applied to moral theology) could translate into mathematical language, and can be analysed against the background of the accounts of (...) probability, pre-mathematical Jesuit logic, Wolff's conceptual analysis, and Bernoullian mathematisation. The works of two Jesuit philosophers, Berthold Hauser and Sigismund Storchenau, can be related to this context. The core of their logic of (epistemic) probability is the account of negation (or ‘contradiction’) and implication (or ‘argument’), in particular, the algorithms for computing the reliability of one piece of evidence when compared to the respective counter-evidence and for computing the probability of a conclusion given the probability of its premises. (shrink)

The area of smart power grids needs to constantly improve its efficiency and resilience, to provide high quality electrical power in a resilient grid, while managing faults and avoiding failures. Achieving this requires high component reliability, adequate maintenance, and a studied failure occurrence. Correct system operation involves those activities and novel methodologies to detect, classify, and isolate faults and failures and model and simulate processes with predictive algorithms and analytics. In this paper, we showcase the application of a complex-adaptive, (...) self-organizing modeling method, and Probabilistic Boolean Networks, as a way towards the understanding of the dynamics of smart grid devices, and to model and characterize their behavior. This work demonstrates that PBNs are equivalent to the standard Reinforcement Learning Cycle, in which the agent/model has an interaction with its environment and receives feedback from it in the form of a reward signal. Different reward structures were created to characterize preferred behavior. This information can be used to guide the PBN to avoid fault conditions and failures. (shrink)

The Next Release Problem (NRP) is a combinatorial optimization problem that aims to find a subset of software requirements to be delivered in the next software release, which maximize the satisfaction of a list of clients and minimize the effort required by developers to implement them. Previous studies have applied various metaheuristics, mostly genetic algorithms. Estimation of Distribution Algorithms (EDA), based on probabilistic modelling, have been proved to obtain good results in problems where genetic algorithms struggle. (...) In this paper we propose to adapt three EDAs to tackle the multi-objective NRP in a fast and effective way. Results show that EDAs can be applicable to solve the NRP with rather good quality of solutions. Furthermore, we prove that their execution time can be significantly reduced using a per-iteration solution subset selection method while maintaining the overall quality of the solutions obtained, and they perform the best when limiting the search time as in an interactive tool that requires fast responsiveness. The experimental framework, code and datasets have been made public in a code repository. (shrink)

The notion of efficient proof-checking has always been central to complexity theory, and it gave rise to the definition of the class NP. In the last 15 years there has been a number of exciting, unexpected and deep developments in complexity theory that exploited the notion of randomized and interactive proof-checking. Results developed along this line of research have diverse and powerful applications in complexity theory, cryptography, and the theory of approximation algorithms for combinatorial optimization problems. In this paper (...) we survey the main lines of developments in interactive and probabilistic proof-checking, with an emphasis on open questions. (shrink)

This article recapitulates and develops the attempts in the Nietzschean traditions to address and overcome the proliferation of nihilism that Nietzsche predicted to unfold in the next 200 years (WP 2). Nietzsche approached nihilism not merely as a psychology but as a labyrinthic and pervasive historical process whereby the highest values of culture and founding assumptions of philosophical thought prevented the further flourishing of life. Therefore, he thought nihilism had to be encountered and experienced on many, often opposing, fronts to (...) be fully consumed and left behind. Thus, just as Nietzsche captured the subtle reinventions of nihilism in new forms in his time, in the new doers assumed behind new deeds (WP 488), this article focuses on the contemporary tectonic shifts brought by digital technology and challenges subjectivation and narrativization of algorithmic will to power in human-like interfaces such as ChatGPT. Having identified philosophers and himself as the most advanced nihilists in their overvaluation of truth, in the 4th part of Thus Spoke Zarathustra, Nietzsche grappled with the difficult, perhaps impossible, temporality of post-nihilistic historicity that oscillates between highest creativity and highest truths, especially in the sections entitled The Shadow and At Noon whereby he explored new temporal techniques to evade the relapses into temporal nihilisms of the notions of linear progress or eternity (TSZ, 4). By drawing on this juncture, this article offers ways to address transfigurations of nihilism behind new technological performances of subjectivity. The article points toward creative temporalities beyond narrativity and subjectivity insofar as the statistical operations and probabilistic estimations of language-models exceed grammatical construction of meaning. This multifaceted application of his thought on the contemporary ontic reality is necessary to perceive our comet's incalculable movement as a veritable ray of sunshine. (shrink)

Di erent from existing reinforcement learning algorithms that generate only reactive policies and existing probabilis tic planning algorithms that requires a substantial amount of a priori knowledge in order to plan we devise a two stage bottom up learning to plan process in which rst reinforce ment learning dynamic programming is applied without the use of a priori domain speci c knowledge to acquire a reactive policy and then explicit plans are extracted from the learned reactive policy Plan (...) extraction is based on a beam search algorithm that performs temporal projection in a restricted fashion guided by the value functions re sulting from reinforcement learning dynamic programming Experiments and theoretical analysis are presented.. (shrink)

Mind and environment evolve in tandem—almost a platitude. Much of judgment and decision making research, however, has compared cognition to standard statistical models, rather than to how well it is adapted to its environment. The author argues two points. First, cognitive algorithms are tuned to certain information formats, most likely to those that humans have encountered during their evolutionary history. In par ticular, Bayesian computations are simpler when the information is in a frequency format than when it is in (...) a probability format. The author investigates whether fre quency formats can make physicians reason more often the Bayesian way. Second, cognitive algorithms need to operate under constraints of limited time, knowledge, and computational power, and they need to exploit the structures of their environments. The author describes a fast and frugal algorithm, Take The Best, that violates standard principles of rational inference but can be as accurate as sophisticated "optimal" mod els for diagnostic inference. Key words: Bayes' theorem; bounded rationality; infor mation format; probabilistic reasoning; satisficing; training; medical education. (shrink)

In this survey we discuss work of Levin and V’yugin on collections of sequences that are non-negligible in the sense that they can be computed by a probabilistic algorithm with positive probability. More precisely, Levin and V’yugin introduced an ordering on collections of sequences that are closed under Turing equivalence. Roughly speaking, given two such collections $\mathcal {A}$ and $\mathcal {B}$, $\mathcal {A}$ is below $\mathcal {B}$ in this ordering if $\mathcal {A}\setminus \mathcal {B}$ is negligible. The degree structure (...) associated with this ordering, the Levin–V’yugin degrees, can be shown to be a Boolean algebra, and in fact a measure algebra. We demonstrate the interactions of this work with recent results in computability theory and algorithmic randomness: First, we recall the definition of the Levin–V’yugin algebra and identify connections between its properties and classical properties from computability theory. In particular, we apply results on the interactions between notions of randomness and Turing reducibility to establish new facts about specific LV-degrees, such as the LV-degree of the collection of 1-generic sequences, that of the collection of sequences of hyperimmune degree, and those collections corresponding to various notions of effective randomness. Next, we provide a detailed explanation of a complex technique developed by V’yugin that allows the construction of semi-measures into which computability-theoretic properties can be encoded. We provide two examples of the use of this technique by explicating a result of V’yugin’s about the LV-degree of the collection of Martin-Löf random sequences and extending the result to the LV-degree of the collection of sequences of DNC degree. (shrink)

This study attempts to analyse the relationship between two key psychological variables associated with performance in sports - Self-Determined Motivation and Competitive Anxiety - through Bayesian Networks analysis. We analysed 674 university students/athletes from 44 universities that competed at the University Games in México, with an average age of 21 years (SD = 2.07) and with a mean of 8.61 years’ (SD = 5.15) experience in sports. Methods: Regarding the data analysis, first a CHAID algorithm was carried out to determine (...) the dependence links between variables, and then a Bayesian networks was developed. The validation of the BN revealed AUC values ranging from 0.5 to 0.92. Subsequently, various instantiations were performed with hypothetical values applied to the “bottom” variables. Results showed two probability trees that have extrinsic motivation and amotivation at the top, while the anxiety/activation due to worries about performance was at the bottom of the probabilities. The instantiations carried out support the existence of these probabilistic relationships, demonstrating their scarce influence on anxiety about competition generated by the intrinsic motivation, and the complex probabilistic effect of introjected and identified regulation regarding the appearance of anxiety due to worry about performance. (shrink)

Many problems in Multi-Agent Systems (MASs) research are formulated in terms of the abilities of a coalition of agents. Existing approaches to reasoning about coalitional ability are usually focused on games or transition systems, which are described in terms of states and actions. Such approaches however often neglect a key feature of multi-agent systems, namely that the actions of the agents require resources. In this paper, we describe a logic for reasoning about coalitional ability under resource constraints in the (...) class='Hi'>probabilistic setting. We extend Resource-bounded Alternating-time Temporal Logic (RB-ATL) with probabilistic reasoning and provide a standard algorithm for the model-checking problem of the resulting logic Probabilistic resource-bounded ATL (pRB-ATL). We implement model-checking algorithms and present experimental results using simple multi-agent model-checking problems of increasing complexity. (shrink)

While Ç ´Ò¿ µ methods for parsing probabilistic context-free grammars (PCFGs) are well known, a tabular parsing framework for arbitrary PCFGs which allows for botton-up, topdown, and other parsing strategies, has not yet been provided. This paper presents such an algorithm, and shows its correctness and advantages over prior work. The paper finishes by bringing out the connections between the algorithm and work on hypergraphs, which permits us to extend the presented Viterbi (best parse) algorithm to an inside (total (...) probability) algorithm. (shrink)

How should we combine disagreeing expert judgments on the likelihood of an event? A common solution is simple averaging, which allows independent individual errors to cancel out. However, judgments can be correlated due to an overlap in their information, resulting in a miscalibration in the simple average. Optimal weights for weighted averaging are typically unknown and require past data to estimate reliably. This paper proposes an algorithm to aggregate probabilistic judgments under shared information. Experts are asked to report a (...) prediction and a meta-prediction. The latter is an estimate of the average of other individuals’ predictions. In a Bayesian setup, I show that if average prediction is a consistent estimator, the percentage of predictions and meta-predictions that exceed the average prediction should be the same. An “overshoot surprise” occurs when the two measures differ. The Surprising Overshoot algorithm uses the information revealed in an overshoot surprise to correct for miscalibration in the average prediction. Experimental evidence suggests that the algorithm performs well in moderate to large samples and in aggregation problems where individuals disagree in their predictions. (shrink)

clusions are only probably correct. On the other hand, algorithmic information theory provides a precise mathematical definition of the notion of random or patternless sequence. In this paper we shall describe conditions under which if the sequence of coin tosses in the Solovay– Strassen and Miller–Rabin algorithms is replaced by a sequence of heads and tails that is of maximal algorithmic information content, i.e., has maximal algorithmic randomness, then one obtains an error-free test for primality. These results are only (...) of theoretical interest, since it is a manifestation of the G¨ odel incompleteness phenomenon that it is impossible to “certify” a sequence to be random by means of a proof, even though most sequences have this property. Thus by using certified random sequences one can in principle, but not in practice, convert probabilistic tests for primality into deterministic ones. (shrink)

The probability ranking conclusion is an extension of the absolute form evaluation conclusion. Firstly, the random simulation evaluation model is introduced; then, the general idea of converting the traditional evaluation method to the random simulation evaluation model is analyzed; on this basis, based on the rule of “further ensuring the stability of the ranking chain on the basis of increasing the possibility of the ranking chain,” two methods of solving the probability ranking conclusion are given. Based on the rule of (...) “further guaranteeing the stability of the ranking chain on the basis of improving the likelihood of the ranking chain,” two methods are given to solve the likelihood conclusion. This paper argues that this absolute form of conclusion hinders the approximation of the theory to the essence of the actual problem and is an important reason for the problem of “non-consistency of multi-evaluation conclusions.” To address this problem, a stochastic simulation-based comprehensive evaluation solution algorithm based on the idea of “Monte Carlo simulation” is proposed, and the corresponding ranking method is investigated, which is characterized by generating evaluation conclusions with probability information, and thus has more advantages than the absolute conclusion form in terms of problem interpretability. The method is characterized by the generation of evaluation conclusions with probabilistic information and thus has more advantages than the absolute conclusion form in terms of problem interpretation. Because of the independence of the stochastic simulation solution method, it is applied to the “bottom-up” evaluation model as an example, and a novel autonomous evaluation method is constructed. Finally, the application of the stochastic simulation evaluation model is illustrated by an example and compared with the absolute form evaluation. The evaluation model is an extension of the traditional evaluation model, which can further broaden the practical application of comprehensive evaluation theory. (shrink)

In this paper we discuss the process of building a joint probability distribution from an input set of low-dimensional probability distributions. Since the solution of the problem for a consistent input set of probability distributions is known we concentrate on a setup where the input probability distributions are inconsistent. In this case the iterative proportional fitting procedure (IPFP), which converges in the consistent case, tends to come to cycles. We propose a new algorithm that converges even in inconsistent case. The (...) important property of the algorithm is that it can be efficiently implemented exploiting decomposability of considered distributions. (shrink)

Probabilistic predictions of future risk govern much of society: healthcare, genetics, social media, national security, and finance. Both policy-makers and private companies are increasingly working to design institutional structures that seek to manage risk by controlling the behavior of citizens and consumers, using new technologies of predictive control that comb through past data to predict and shape future action. These predictions not only control social institutions but also shape individual character and forms of practical reason. Risk-based decision theory shifts (...) people's relationships to the future through knowledge of possible dangers and foregone opportunities, thus inspiring anxious solicitude and deceptive hopes for total security. This book uses virtue ethics to analyze these problems and to suggest ways to enjoy these technologies' positive benefits while constraining their dangerous aspects through a better understanding of practical reasoning and a theological analysis of our responsibility for future risks. (shrink)

A set of infinite binary sequences ${\cal C} \subseteq 2$ℕ is negligible if there is no partial probabilistic algorithm that produces an element of this set with positive probability. The study of negligibility is of particular interest in the context of ${\rm{\Pi }}_1^0 $ classes. In this paper, we introduce the notion of depth for ${\rm{\Pi }}_1^0 $ classes, which is a stronger form of negligibility. Whereas a negligible ${\rm{\Pi }}_1^0 $ class ${\cal C}$ has the property that one (...) cannot probabilistically compute a member of ${\cal C}$ with positive probability, a deep ${\rm{\Pi }}_1^0 $ class ${\cal C}$ has the property that one cannot probabilistically compute an initial segment of a member of ${\cal C}$ with high probability. That is, the probability of computing a length n initial segment of a deep ${\rm{\Pi }}_1^0 $ class converges to 0 effectively in n.We prove a number of basic results about depth, negligibility, and a variant of negligibility that we call tt-negligibility. We provide a number of examples of deep ${\rm{\Pi }}_1^0 $ classes that occur naturally in computability theory and algorithmic randomness. We also study deep classes in the context of mass problems, examine the relationship between deep classes and certain lowness notions in algorithmic randomness, and establish a relationship between members of deep classes and the amount of mutual information with Chaitin’s Ω. (shrink)

We argue that certain types of many minds (and many worlds) interpretations of quantum mechanics, e.g. Lockwood ([1996a]), Deutsch ([1985]) do not provide a coherent interpretation of the quantum mechanical probabilistic algorithm. By contrast, in Albert and Loewer's ([1988]) version of the many minds interpretation, there is a coherent interpretation of the quantum mechanical probabilities. We consider Albert and Loewer's probability interpretation in the context of Bell-type and GHZ-type states and argue that it implies a certain (weak) form of (...) nonlocality. 1 Introduction 2 Albert and Loewer's interpretation 3 Probabilities in Lockwood's interpretation 4 Sets of minds and their correlations 5 Many minds and GHZ. (shrink)

Prelinguistic infants must find a way to isolate meaningful chunks from the continuous streams of speech that they hear. BootLex, a new model which uses distributional cues to build a lexicon, demonstrates how much can be accomplished using this single source of information. This conceptually simple probabilistic algorithm achieves significant segmentation results on various kinds of language corpora - English, Japanese, and Spanish; child- and adult-directed speech, and written texts; and several variations in coding structure - and reveals which (...) statistical characteristics of the input have an influence on segmentation performance. BootLex is then compared, quantitatively and qualitatively, with three other groups of computational models of the same infant segmentation process, paying particular attention to functional characteristics of the models and their similarity to human cognition. Commonalities and contrasts among the models are discussed, as well as their implications both for theories of the cognitive problem of segmentation itself, and for the general enterprise of computational cognitive modeling. (shrink)

In this article I discuss the attribution of photographic indexicality to synthetic photorealistically rendered images. For some traditionalists the idea of photographic indexicality being associated with a synthetically produced digital image is heresy, while others who are more comfortable with the attribution will look to the underlying computational methods that lie behind this insight. An examination of the underpinnings of the software algorithms that produce these synthetic images points to a class of statistical methods based on Monte Carlo simulation, (...) which employs nondeterministic randomness as a strategy to overcome the overwhelming complexity of the simulations. Expanding on a practice that uses the instrumental nature of these probabilistic algorithms as a means to examine the aesthetic qualities of simulated light, I suggest that these mathematically incomplete simulations capture a referential linkage between subject and image – equivalent to a form of indexicality. (shrink)

Soon after the first COVID-19 positive case was detected in Wuhan, China, the virus spread around the globe, and in no time, it was declared as a global pandemic by the WHO. Testing, which is the first step in identifying and diagnosing COVID-19, became the first need of the masses. Therefore, testing kits for COVID-19 were manufactured for efficiently detecting COVID-19. However, due to limited resources in the densely populated countries, testing capacity even after a year is still a limiting (...) factor for COVID-19 diagnosis on a larger scale and contributes to a lag in disease tracking and containment. Due to this reason, we started this study to provide a better cost-effective solution for enhancing the testing capacity so that the maximum number of people could get tested for COVID-19. For this purpose, we utilized the approach of artificial neural networks (ANN) to acquire the relevant data on COVID-19 and its testing. The data were analyzed by using Machine Learning, and probabilistic algorithms were applied to obtain a statistically proven solution for COVID-19 testing. The results obtained through ANN indicated that sample pooling is not only an effective way but also regarded as a “Gold standard” for testing samples when the prevalence of the disease is low in the population and the chances of getting a positive result are less. We further demonstrated through algorithms that pooling samples from 16 individuals is better than pooling samples of 8 individuals when there is a high likelihood of getting negative test results. These findings provide ground to the fact that if sample pooling will be employed on a larger scale, testing capacity will be considerably increased within limited available resources without compromising the test specificity. It will provide healthcare units and enterprises with solutions through scientifically proven algorithms, thus, saving a considerable amount of time and finances. This will eventually help in containing the spread of the pandemic in densely populated areas including vulnerably confined groups, such as nursing homes, hospitals, cruise ships, and military ships. (shrink)