A common computational and neural anomaly across mouse models of autism.

Computational psychiatry has suggested that humans within the autism spectrum disorder (ASD) inflexibly update their expectations (i.e., Bayesian priors). Here, we leveraged high-yield rodent psychophysics (n = 75 mice), extensive behavioral modeling (including principled and heuristics), and (near) brain-wide single cell extracellular recordings (over 53k units in 150 brain areas) to ask (1) whether mice with different genetic perturbations associated with ASD show this same computational anomaly, and if so, (2) what neurophysiological features are shared across genotypes in subserving this deficit. We demonstrate that mice harboring mutations in Fmr1 , Cntnap2 , and Shank3B show a blunted update of priors during decision-making. Neurally, the differentiating factor between animals flexibly and inflexibly updating their priors was a shift in the weighting of prior encoding from sensory to frontal cortices. Further, in mouse models of ASD frontal areas showed a preponderance of units coding for deviations from the animals' long-run prior, and sensory responses did not differentiate between expected and unexpected observations. These findings demonstrate that distinct genetic instantiations of ASD may yield common neurophysiological and behavioral phenotypes.

Uncertainty is maintained and used in working memory.

What are the contents of working memory? In both behavioral and neural computational models, a working memory representation is typically described by a single number, namely, a point estimate of a stimulus. Here, we asked if people also maintain the uncertainty associated with a memory and if people use this uncertainty in subsequent decisions. We collected data in a two-condition orientation change detection task; while both conditions measured whether people used memory uncertainty, only one required maintaining it. For each condition, we compared an optimal Bayesian observer model, in which the observer uses an accurate representation of uncertainty in their decision, to one in which the observer does not. We find that this "Use Uncertainty" model fits better for all participants in both conditions. In the first condition, this result suggests that people use uncertainty optimally in a working memory task when that uncertainty information is available at the time of decision, confirming earlier results. Critically, the results of the second condition suggest that this uncertainty information was maintained in working memory. We test model variants and find that our conclusions do not depend on our assumptions about the observer's encoding process, inference process, or decision rule. Our results provide evidence that people have uncertainty that reflects their memory precision on an item-specific level, maintain this information over a working memory delay, and use it implicitly in a way consistent with an optimal observer. These results challenge existing computational models of working memory to update their frameworks to represent uncertainty.

Unbiased and efficient log-likelihood estimation with inverse binomial sampling.

The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter estimation and model evaluation. However, the log-likelihood of complex models in fields such as computational biology and neuroscience is often intractable to compute analytically or numerically. In those cases, researchers can often only estimate the log-likelihood by comparing observed data with synthetic observations generated by model simulations. Standard techniques to approximate the likelihood via simulation either use summary statistics of the data or are at risk of producing substantial biases in the estimate. Here, we explore another method, inverse binomial sampling (IBS), which can estimate the log-likelihood of an entire data set efficiently and without bias. For each observation, IBS draws samples from the simulator model until one matches the observation. The log-likelihood estimate is then a function of the number of samples drawn. The variance of this estimator is uniformly bounded, achieves the minimum variance for an unbiased estimator, and we can compute calibrated estimates of the variance. We provide theoretical arguments in favor of IBS and an empirical assessment of the method for maximum-likelihood estimation with simulation-based models. As case studies, we take three model-fitting problems of increasing complexity from computational and cognitive neuroscience. In all problems, IBS generally produces lower error in the estimated parameters and maximum log-likelihood values than alternative sampling methods with the same average number of samples. Our results demonstrate the potential of IBS as a practical, robust, and easy to implement method for log-likelihood evaluation when exact techniques are not available.

The role of sensory uncertainty in simple contour integration.

Perceptual organization is the process of grouping scene elements into whole entities. A classic example is contour integration, in which separate line segments are perceived as continuous contours. Uncertainty in such grouping arises from scene ambiguity and sensory noise. Some classic Gestalt principles of contour integration, and more broadly, of perceptual organization, have been re-framed in terms of Bayesian inference, whereby the observer computes the probability that the whole entity is present. Previous studies that proposed a Bayesian interpretation of perceptual organization, however, have ignored sensory uncertainty, despite the fact that accounting for the current level of perceptual uncertainty is one of the main signatures of Bayesian decision making. Crucially, trial-by-trial manipulation of sensory uncertainty is a key test to whether humans perform near-optimal Bayesian inference in contour integration, as opposed to using some manifestly non-Bayesian heuristic. We distinguish between these hypotheses in a simplified form of contour integration, namely judging whether two line segments separated by an occluder are collinear. We manipulate sensory uncertainty by varying retinal eccentricity. A Bayes-optimal observer would take the level of sensory uncertainty into account-in a very specific way-in deciding whether a measured offset between the line segments is due to non-collinearity or to sensory noise. We find that people deviate slightly but systematically from Bayesian optimality, while still performing "probabilistic computation" in the sense that they take into account sensory uncertainty via a heuristic rule. Our work contributes to an understanding of the role of sensory uncertainty in higher-order perception.

Human online adaptation to changes in prior probability.

Optimal sensory decision-making requires the combination of uncertain sensory signals with prior expectations. The effect of prior probability is often described as a shift in the decision criterion. Can observers track sudden changes in probability? To answer this question, we used a change-point detection paradigm that is frequently used to examine behavior in changing environments. In a pair of orientation-categorization tasks, we investigated the effects of changing probabilities on decision-making. In both tasks, category probability was updated using a sample-and-hold procedure: probability was held constant for a period of time before jumping to another probability state that was randomly selected from a predetermined set of probability states. We developed an ideal Bayesian change-point detection model in which the observer marginalizes over both the current run length (i.e., time since last change) and the current category probability. We compared this model to various alternative models that correspond to different strategies-from approximately Bayesian to simple heuristics-that the observers may have adopted to update their beliefs about probabilities. While a number of models provided decent fits to the data, model comparison favored a model in which probability is estimated following an exponential averaging model with a bias towards equal priors, consistent with a conservative bias, and a flexible variant of the Bayesian change-point detection model with incorrect beliefs. We interpret the former as a simpler, more biologically plausible explanation suggesting that the mechanism underlying change of decision criterion is a combination of on-line estimation of prior probability and a stable, long-term equal-probability prior, thus operating at two very different timescales.

Bayesian comparison of explicit and implicit causal inference strategies in multisensory heading perception.

The precision of multisensory perception improves when cues arising from the same cause are integrated, such as visual and vestibular heading cues for an observer moving through a stationary environment. In order to determine how the cues should be processed, the brain must infer the causal relationship underlying the multisensory cues. In heading perception, however, it is unclear whether observers follow the Bayesian strategy, a simpler non-Bayesian heuristic, or even perform causal inference at all. We developed an efficient and robust computational framework to perform Bayesian model comparison of causal inference strategies, which incorporates a number of alternative assumptions about the observers. With this framework, we investigated whether human observers' performance in an explicit cause attribution and an implicit heading discrimination task can be modeled as a causal inference process. In the explicit causal inference task, all subjects accounted for cue disparity when reporting judgments of common cause, although not necessarily all in a Bayesian fashion. By contrast, but in agreement with previous findings, data from the heading discrimination task only could not rule out that several of the same observers were adopting a forced-fusion strategy, whereby cues are integrated regardless of disparity. Only when we combined evidence from both tasks we were able to rule out forced-fusion in the heading discrimination task. Crucially, findings were robust across a number of variants of models and analyses. Our results demonstrate that our proposed computational framework allows researchers to ask complex questions within a rigorous Bayesian framework that accounts for parameter and model uncertainty.

Target Uncertainty Mediates Sensorimotor Error Correction.

Human movements are prone to errors that arise from inaccuracies in both our perceptual processing and execution of motor commands. We can reduce such errors by both improving our estimates of the state of the world and through online error correction of the ongoing action. Two prominent frameworks that explain how humans solve these problems are Bayesian estimation and stochastic optimal feedback control. Here we examine the interaction between estimation and control by asking if uncertainty in estimates affects how subjects correct for errors that may arise during the movement. Unbeknownst to participants, we randomly shifted the visual feedback of their finger position as they reached to indicate the center of mass of an object. Even though participants were given ample time to compensate for this perturbation, they only fully corrected for the induced error on trials with low uncertainty about center of mass, with correction only partial in trials involving more uncertainty. The analysis of subjects' scores revealed that participants corrected for errors just enough to avoid significant decrease in their overall scores, in agreement with the minimal intervention principle of optimal feedback control. We explain this behavior with a term in the loss function that accounts for the additional effort of adjusting one's response. By suggesting that subjects' decision uncertainty, as reflected in their posterior distribution, is a major factor in determining how their sensorimotor system responds to error, our findings support theoretical models in which the decision making and control processes are fully integrated.

On the origins of suboptimality in human probabilistic inference.

Humans have been shown to combine noisy sensory information with previous experience (priors), in qualitative and sometimes quantitative agreement with the statistically-optimal predictions of Bayesian integration. However, when the prior distribution becomes more complex than a simple Gaussian, such as skewed or bimodal, training takes much longer and performance appears suboptimal. It is unclear whether such suboptimality arises from an imprecise internal representation of the complex prior, or from additional constraints in performing probabilistic computations on complex distributions, even when accurately represented. Here we probe the sources of suboptimality in probabilistic inference using a novel estimation task in which subjects are exposed to an explicitly provided distribution, thereby removing the need to remember the prior. Subjects had to estimate the location of a target given a noisy cue and a visual representation of the prior probability density over locations, which changed on each trial. Different classes of priors were examined (Gaussian, unimodal, bimodal). Subjects' performance was in qualitative agreement with the predictions of Bayesian Decision Theory although generally suboptimal. The degree of suboptimality was modulated by statistical features of the priors but was largely independent of the class of the prior and level of noise in the cue, suggesting that suboptimality in dealing with complex statistical features, such as bimodality, may be due to a problem of acquiring the priors rather than computing with them. We performed a factorial model comparison across a large set of Bayesian observer models to identify additional sources of noise and suboptimality. Our analysis rejects several models of stochastic behavior, including probability matching and sample-averaging strategies. Instead we show that subjects' response variability was mainly driven by a combination of a noisy estimation of the parameters of the priors, and by variability in the decision process, which we represent as a noisy or stochastic posterior.

Internal representations of temporal statistics and feedback calibrate motor-sensory interval timing.

Humans have been shown to adapt to the temporal statistics of timing tasks so as to optimize the accuracy of their responses, in agreement with the predictions of Bayesian integration. This suggests that they build an internal representation of both the experimentally imposed distribution of time intervals (the prior) and of the error (the loss function). The responses of a Bayesian ideal observer depend crucially on these internal representations, which have only been previously studied for simple distributions. To study the nature of these representations we asked subjects to reproduce time intervals drawn from underlying temporal distributions of varying complexity, from uniform to highly skewed or bimodal while also varying the error mapping that determined the performance feedback. Interval reproduction times were affected by both the distribution and feedback, in good agreement with a performance-optimizing Bayesian observer and actor model. Bayesian model comparison highlighted that subjects were integrating the provided feedback and represented the experimental distribution with a smoothed approximation. A nonparametric reconstruction of the subjective priors from the data shows that they are generally in agreement with the true distributions up to third-order moments, but with systematically heavier tails. In particular, higher-order statistical features (kurtosis, multimodality) seem much harder to acquire. Our findings suggest that humans have only minor constraints on learning lower-order statistical properties of unimodal (including peaked and skewed) distributions of time intervals under the guidance of corrective feedback, and that their behavior is well explained by Bayesian decision theory.

Is the prevalence of overweight reducing at age 5-6 years? Ten years data collection in ASL Milano 2.

BACKGROUND: Prevalence of overweight and obesity has been reported as high even in preschool age children. However, recent international reports suggest that prevalence is now plateauing in pediatric age. Up to now no data are available on prevalence changes in Italy in the new Millennium. Aim of the study was to describe changes of overweight and obesity prevalence during the last decade in 5-6 y children in a large Health Unit in Northern Italy. METHODS: The Health Report n 8, used at 5-6 y and containing body mass index (BMI), was utilized for prevalence estimation from 2002 to 2011 according to BMI cut-offs proposed by Cole et al. RESULTS: Overweight and obese children progressively decreased during the study period (p 0.0002) with a minimum observed in 2011, showing a cumulative frequency of 23.1% in 2002 and of 16.6% in 2011 (-6.5%). Mean BMI values progressively decreased with time so that BMI values in 2010-2011 were significantly lower than in 2002-2003 (p < 0.0001). Underweight subjects increased with time (p 0.013), from 8.2% in 2002 to 9.9% in 2011, but grade 3 underweight (i.e., severe thinness) did not increase during the study period. In years 2010 plus 2011, not Italians children showed higher percentages of underweight (12.5%) and overweight plus obesity (23.5%) respect to Italian peers (9.0% and 18.1%, respectively, p values <0.01 and 0.0029). CONCLUSIONS: This is the first report suggesting a possible decrease of overweight and obesity at 5-6 y in Italy in the last decade. As the study focused only on 5-6 y children, we don't know if the true overweight prevalence in pediatric age is really reducing or the starting age of overweight status is simply delayed. The higher risk for malnutrition, both for excess or defect, found in our Area in not Italian children respect to Italian peers, strongly suggests to implement weight control especially for those children. Our finding needs further confirm studies but seems encouraging for true prevention of such condition.

[Usefulness of the 5-6-yrs-old anthropometric health report for the evaluation of childhood overweight and obesity: pilot study in Lombardia (Italy)]. / Utilità della scheda bilancio di salute per la rilevazione di sovrappeso e obesità nei bambini tra 5 e 6 anni: esperienza pilota in Lombardia.

OBJECTIVE: To verify the possibility to use the Anthropometric Health Report (AHR), containing the BMI value, for overweight/obesity evaluation in 5-6-years-old children. DESIGN: Between January 2001 and December 2004, 4619 AHR had been examined. BMI values were compared with age and sex-specific BMI cutoffs, according to Cole, as well as with a single BMI value, calculated as the mean between boys and girls cutoff at 5.5 yrs of age. SETTING: 4619 children of ASL Provincia di Milano 2, aged 5-6 years were examined. PARTECIPANTS: 81 Family Pediatricians working in the area of Provincia di Milano 2. MAIN OUTCOME MEASURES: An easily available and low cost method for epidemiological studies on overweight and obesity in childhood. RESULTS: During the study period the number of examined children increased constantly (from 8% to 30% of the overall resident population). Also the correct compilation of the AHR raised (from 47% to 95%). The elevated percentage of overweight children (range 17-23%) and obese children (range 5-7%) in the study group confirms other published data in this age group. The use of a single BMI cutoff did not affect significantly (p > 0.05) the results with regard to the use ofage and sex-specific cut offs. Required time for carrying out the study was limited. Efficiency increased during the study: the number ofAHRs analyzed per hour increased from 37.5 in 2001 to 103.5 in 2004. Some critical points about current uses of AHR are discussed CONCLUSIONS: AHR could be used for epidemiological purposes. It could be considered an useful method in monitoring overweight/obesity in 5-6 years old children as well as in checking the efficacy of prevention and therapeutic strategies.