Forecasting electricity consumption by aggregating specialized experts

33 pagesInternational audienceWe consider the setting of sequential prediction of arbitrary sequences based on specialized experts. We first provide a review of the relevant literature and present two theoretical contributions: a general analysis of the specialist aggregation rule of Freund et al. (1997) and an adaptation of fixed-share rules of Herbster and Warmuth (1998) in this setting. We then apply these rules to the sequential short-term (one-day-ahead) forecasting of electricity consumption; to do so, we consider two data sets, a Slovakian one and a French one, respectively concerned with hourly and half-hourly predictions. We follow a general methodology to perform the stated empirical studies and detail in particular tuning issues of the learning parameters. The introduced aggregation rules demonstrate an improved accuracy on the data sets at hand; the improvements lie in a reduced mean squared error but also in a more robust behavior with respect to large occasional errors

Learning about and from others' prudence, impatience or laziness: The computational bases of attitude alignment

<div><p>Peoples' subjective attitude towards costs such as, e.g., risk, delay or effort are key determinants of inter-individual differences in goal-directed behaviour. Thus, the ability to learn about others' prudent, impatient or lazy attitudes is likely to be critical for social interactions. Conversely, how adaptive such attitudes are in a given environment is highly uncertain. Thus, the brain may be tuned to garner information about how such costs ought to be arbitrated. In particular, observing others' attitude may change one's uncertain belief about how to best behave in related difficult decision contexts. In turn, learning <i>from</i> others' attitudes is determined by one's ability to learn <i>about</i> others' attitudes. We first derive, from basic optimality principles, the computational properties of such a learning mechanism. In particular, we predict two apparent cognitive biases that would arise when individuals are learning about others’ attitudes: (i) people should overestimate the degree to which they resemble others (false-consensus bias), and (ii) they should align their own attitudes with others’ (social influence bias). We show how these two biases non-trivially interact with each other. We then validate these predictions experimentally by profiling people's attitudes both before and after guessing a series of cost-benefit arbitrages performed by calibrated artificial agents (which are impersonating human individuals).</p></div

Computational mechanisms of theory of mind

Les hommes semblent dotés d'une capacité fascinante : celle d'attribuer des croyances et des désirs aux autres afin d'expliquer leur comportement. Cette capacité, appelée Théorie de l'Esprit, nous permet de résoudre un problème complexe : à partir de la seule observation de leurs faits et gestes, nous déduisons les états mentaux qui poussent les autres à agir. Dans cette thèse, nous formalisons ce problème et en proposons une solution se fondant sur l'inférence bayésienne. Nous appliquons ce cadre théorique à deux situations particulières : l'attribution de croyances récursives en situations d'interaction sociale et l'apprentissage des préférences des autres. En combinant modèles computationnels et expériences comportementales, nous abordons avec une nouvelle perspective certaines questions fondamentales soulevées par l'étude de la Théorie de l'Esprit. Sommes-nous optimaux lorsque nous attribuons des croyances et des préférences aux autres ? Employons-nous des processus spécifiques quand nous interagissons avec d'autres personnes ? Quelles sont les contraintes évolutionnaires qui ont donné forme à notre Théorie de l'Esprit ? Cette capacité est-elle spécifiquement humaine ? Comment la Théorie de l'Esprit est-elle affectée dans l'autisme ?Human beings have this surprising ability – coined Theory of Mind (ToM) – to reason about the mind of others and interpret their behaviour in terms of beliefs and desires. In this thesis, we focus on two critical aspects of ToM: (1) our ability to attribute recursive beliefs of the type “I think that you think that I think...” in the context of social interactions, (2) our ability to infer other people’s personal characteristics or preferences from observing their choices. This computational characterization of mechanisms at play in ToM provides new tools to address important questions such as: What is specific about learning in a context of social interactions? Are we optimal in our inference about others’ preferences or beliefs? Can we identify evolutionary constraints that may have shaped our current sophistication in ToM? Are these processes uniquely human? In which ways is ToM affected in disorders involving difficulties with social interactions? We investigated these questions combining computational modelling and behavioural experiments. The results of our studies offer significant advances in the description of the computational mechanisms underlying social cognition in humans and in non-human primates. Moreover, applying our paradigms to people from the autistic spectrum disorder allowed us to characterize what makes social cognition in autism so different

Social behavioural adaptation in Autism.

Autism is still diagnosed on the basis of subjective assessments of elusive notions such as interpersonal contact and social reciprocity. We propose to decompose reciprocal social interactions in their basic computational constituents. Specifically, we test the assumption that autistic individuals disregard information regarding the stakes of social interactions when adapting to others. We compared 24 adult autistic participants to 24 neurotypical (NT) participants engaging in a repeated dyadic competitive game against artificial agents with calibrated reciprocal adaptation capabilities. Critically, participants were framed to believe either that they were competing against somebody else or that they were playing a gambling game. Only the NT participants did alter their adaptation strategy when they held information regarding others' competitive incentives, in which case they outperformed the AS group. Computational analyses of trial-by-trial choice sequences show that the behavioural repertoire of autistic people exhibits subnormal flexibility and mentalizing sophistication, especially when information regarding opponents' incentives was available. These two computational phenotypes yield 79% diagnosis classification accuracy and explain 62% of the severity of social symptoms in autistic participants. Such computational decomposition of the autistic social phenotype may prove relevant for drawing novel diagnostic boundaries and guiding individualized clinical interventions in autism

Theory of mind: did evolution fool us?

Theory of Mind (ToM) is the ability to attribute mental states (e.g., beliefs and desires) to other people in order to understand and predict their behaviour. If others are rewarded to compete or cooperate with you, then what they will do depends upon what they believe about you. This is the reason why social interaction induces recursive ToM, of the sort "I think that you think that I think, etc.". Critically, recursion is the common notion behind the definition of sophistication of human language, strategic thinking in games, and, arguably, ToM. Although sophisticated ToM is believed to have high adaptive fitness, broad experimental evidence from behavioural economics, experimental psychology and linguistics point towards limited recursivity in representing other's beliefs. In this work, we test whether such apparent limitation may not in fact be proven to be adaptive, i.e. optimal in an evolutionary sense. First, we propose a meta-Bayesian approach that can predict the behaviour of ToM sophistication phenotypes who engage in social interactions. Second, we measure their adaptive fitness using evolutionary game theory. Our main contribution is to show that one does not have to appeal to biological costs to explain our limited ToM sophistication. In fact, the evolutionary cost/benefit ratio of ToM sophistication is non trivial. This is partly because an informational cost prevents highly sophisticated ToM phenotypes to fully exploit less sophisticated ones (in a competitive context). In addition, cooperation surprisingly favours lower levels of ToM sophistication. Taken together, these quantitative corollaries of the "social Bayesian brain" hypothesis provide an evolutionary account for both the limitation of ToM sophistication in humans as well as the persistence of low ToM sophistication levels

Assessment of the relationship between false-consensus and influence biases.

<p>This figure summarizes the attempt to validate the prediction summarized on <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005422#pcbi.1005422.g002" target="_blank">Fig 2D</a>. <b>A:</b> participants' influence bias (y-axis) is plotted as a function of their false-consensus bias <i>FCB</i> (x-axis), in the <i>Different</i> condition, across all cost types. The data have been binned according to <i>FCB</i>, and blue error bars depict the resulting mean and standard errors around the mean. The red line depicts the best fitting quadratic expansion. <b>B:</b> Same as in A, but this time with influence biases corrected for age and gender inter-individual variability.</p

Does the way we read others' mind change over the lifespan? Insights from a massive web poll of cognitive skills from childhood to late adulthood

Mentalizing or Theory of Mind (ToM), i.e., the ability to recognize what people think or feel, is a crucial component of human social intelligence. It has been recently proposed that ToM can be decomposed into automatic and controlled neurocognitive components, where only the latter engage executive functions (e.g., working memory, inhibitory control and task switching). Critical here is the notion that such dual processes are expected to follow different developmental dynamics. In this work, we provide novel experimental evidence for this notion. We report data gathered from about thirty thousand participants of a massive web poll of people's cognitive skills, which included ToM and executive functions. We show that although the maturation of executive functions occurs in synchrony (around 20 years of age), this is not the case for different mentalizing competences, which either mature before (for elementary ToM constituents) or after (for higher-level ToM). In addition, we show that inter-individual differences in executive functions predict variability in higher-level ToM skills from the onset of adulthood onwards, i.e., after the complete maturation of executive functions. Taken together, these results indicate that the relative contribution of ToM's controlled component significantly changes with age. In particular, this implies that, over the lifespan, people may rely upon distinct cognitive architectures when reading others' minds

Response of the BPL model.

<p>We simulated virtual BPL learners equipped with neutral priors (), who learned about agents (endowed with varying cost-susceptibilities) performing cost-benefit arbitrages (<i>T</i> = 40 choices, as in the main experiment). The Monte-Carlo average (plain lines) and standard deviations (shaded areas) of BPL's posterior estimates were obtained by repeating this simulation with random pairings of benefits and costs. We also varied BPL's prior variance on the Other's cost susceptibility (blue: small prior variance, red: high prior variance). <b>A:</b> BPL's posterior estimate of the Other's cost-susceptibility (y-axis) is plotted as a function of the true Other's cost-susceptibility (x-axis). <b>B</b>: BPL's posterior estimate of the Other's inverse-temperature (y-axis) is plotted as a function of the true Other's cost-susceptibility (x-axis).</p

Experimental paradigm.

<p><b>A:</b> main structure of the task (<i>Decision 1</i>, <i>Prediction</i> and <i>Decision 2</i> phases). Each phase includes three subtasks, which relate to three cost-benefit arbitrages (with three cost types, namely: delay, effort or risk, respectively). Participants are partitioned into three subgroups, depending on which cost type is paired with the <i>Noisy</i>, <i>Same</i> or <i>Different</i> condition in the <i>Prediction</i> phase. <b>B:</b> Example trials of cost-benefit arbitrages (Left: Delay, Middle: Effort, Right: Risk). Note: the low-cost/low-reward option is displayed on the left (its associated cost is fixed across trials).</p

Model-free results.

<p>Quantification of false-consensus (A) and influence biases (B), in terms of a comparison between the <i>Same</i> (yellow) and <i>Different</i> (purple) conditions. <b>A: Top:</b> average performance (+/- standard error on the mean) during the <i>Prediction</i> phase is plotted as a function of session stage (beginning/end) and condition type (<i>Same/Different</i>). <b>Bottom:</b> histogram of the ANOVA residuals (grey bars) and moment-matched Gaussian approximation (red line). <b>B: Top:</b> average difference in the number of low-cost choices between <i>Decision</i> phases 1 and 2 (+/- standard error on the mean) is plotted as a function of participants’ initial cost-susceptibility (low/high) and condition type (<i>Same/Different</i>). Note: in the <i>Different</i> condition, participants with an initial high (resp., low) cost-susceptibility have observed an artificial agent endowed with a high (resp., low) cost-susceptibility. <b>Bottom:</b> histogram of the ANOVA residuals (grey bars) and moment-matched Gaussian approximation (red line).</p