Luigi Acerbi PhD

Luigi Acerbi


Research Interests

My main research interest is the role of complex (beyond Gaussian) internal representations of stimulus statistics and other features of probabilistic computation in perceptual decision making. My PhD combines mathematical and computational modelling, machine learning techniques and psychophysical experiments.

At the beginning of my PhD I investigated learning and adaptation phenomena in sensorimotor timing tasks. In particular, in this paper we looked at the role of complex statistical properties of the context (i.e. non-Gaussian priors and non-quadratic loss functions, in Bayesian terms) in calibrating human sensorimotor timing.

My more recent work focusses on the sources of sub-optimality in human probabilistic inference within complex sensorimotor estimation tasks. At the moment I am systematically exploring the implications for behaviour of different assumptions regarding the decision process, sensory and decision noise and the internal representations of statistics (priors).

Publications:
2017
  Target Uncertainty Mediates Sensorimotor Error Correction
Acerbi, L, Vijayakumar, S, Wolpert, DM & Buckingham, G (ed.) 2017, 'Target Uncertainty Mediates Sensorimotor Error Correction' PLoS One, vol 12, no. 1, e0170466, pp. 1-21. DOI: 10.1371/journal.pone.0170466
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.

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General Information
Organisations: School of Informatics.
Authors: Acerbi, Luigi, Vijayakumar, Sethu & Wolpert, Daniel M..
Number of pages: 21
Pages: 1-21
Publication Date: 27 Jan 2017
Publication Information
Category: Article
Journal: PLoS One
Volume: 12
Issue number: 1
ISSN: 1932-6203
Original Language: English
DOIs: 10.1371/journal.pone.0170466
2014
  A matter of uncertainty: Optimality and sub-optimality in sensorimotor learning
Acerbi, L, Vijayakumar, S & Wolpert, D 2014, A matter of uncertainty: Optimality and sub-optimality in sensorimotor learning. in Decision Making Bristol 2014.
General Information
Organisations: Institute of Perception, Action and Behaviour .
Authors: Acerbi, Luigi, Vijayakumar, Sethu & Wolpert, Daniel.
Publication Date: 2014
Publication Information
Category: Conference contribution
Original Language: English
  A Framework for Testing Identifiability of Bayesian Models of Perception
Acerbi, L, Ma, WJ & Vijayakumar, S 2014, A Framework for Testing Identifiability of Bayesian Models of Perception. in Z Ghahramani, M Welling, C Cortes, ND Lawrence & KQ Weinberger (eds), Advances in Neural Information Processing Systems 27. Curran Associates Inc, pp. 1026-1034.
Bayesian observer models are very effective in describing human performance in perceptual tasks, so much so that they are trusted to faithfully recover hidden mental representations of priors, likelihoods, or loss functions from the data. However, the intrinsic degeneracy of the Bayesian framework, as multiple combinations of elements can yield empirically indistinguishable results, prompts the question of model identifiability. We propose a novel framework for a systematic testing of the identifiability of a significant class of Bayesian observer models, with practical applications for improving experimental design. We examine the theoretical identifiability of the inferred internal representations in two case studies. First, we show which experimental designs work better to remove the underlying degeneracy in a time interval estimation task. Second, we find that the reconstructed representations in a speed perception task under a slow-speed prior are fairly robust.
General Information
Organisations: Institute of Perception, Action and Behaviour .
Authors: Acerbi, Luigi, Ma, Wei Ji & Vijayakumar, Sethu.
Number of pages: 9
Pages: 1026-1034
Publication Date: 2014
Publication Information
Category: Conference contribution
Original Language: English
  On the Origins of Suboptimality in Human Probabilistic Inference
Acerbi, L, Vijayakumar, S & Wolpert, DM 2014, 'On the Origins of Suboptimality in Human Probabilistic Inference' PLoS Computational Biology, vol 10, no. 6, 1003661. DOI: 10.1371/journal.pcbi.1003661
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.
General Information
Organisations: Institute of Perception, Action and Behaviour .
Authors: Acerbi, Luigi, Vijayakumar, Sethu & Wolpert, Daniel M..
Keywords: (BAYESIAN-INFERENCE, DECISION-THEORY, PROSPECT-THEORY, PERCEPTION, MOTION, MODEL, TASK, DISTRIBUTIONS, EXPECTATIONS, VARIABILITY. )
Number of pages: 23
Publication Date: Jun 2014
Publication Information
Category: Article
Journal: PLoS Computational Biology
Volume: 10
Issue number: 6
ISSN: 1553-734X
Original Language: English
DOIs: 10.1371/journal.pcbi.1003661
  Probing the sources of suboptimality in human Bayesian inference
Acerbi, L, Wolpert, D & Vijayakumar, S 2014, 'Probing the sources of suboptimality in human Bayesian inference' Computational and Systems Neuroscience (Cosyne) 2014, Salt Lake City, United States, 27/02/14 - 2/03/14, .
When humans are presented with a simple Gaussian distribution of stimuli in an experimental setting, they are often able to combine this prior with noisy sensory information in agreement with the ‘optimal’ solution of Bayesian Decision Theory (BDT). However, in the presence of more complex experimental distributions (e.g. skewed or bimodal) performance appears suboptimal even after extensive training. Such suboptimality could arise from an inaccurate internal representation of the complex prior and/or from limitations in performing probabilistic inference on a veridical internal representation. We tested between these possibilities by developing a novel estimation task in which subjects were provided with explicit probabilistic information on each trial, thereby removing the need to learn the prior. The task consisted of estimating the location of a hidden target given a noisy cue and a visual representation of the prior probability density over locations, which changed from trial to trial. Priors belonged to different classes of distributions such as Gaussian, unimodal and bimodal. Subjects’ performance was in qualitative agreement with the predictions of BDT albeit generally suboptimal. However, the degree of suboptimality was largely independent of both the class of the prior and the level of noise in the cue, suggesting that learning or recalling the prior constitutes more of a challenge to decision making than manipulating the complex probabilistic information. We performed an extensive model comparison across a large set of suboptimal Bayesian observer models. Our analysis rejects many common models of variability in our task, such as probability matching and a sample-averaging strategy. Instead we found that subjects’ suboptimality was driven both by a miscalibrated internal representation of the parameters of the likelihood, and by decision noise that can be interpreted as a noisy representation of the posterior
General Information
Organisations: Institute of Perception, Action and Behaviour .
Authors: Acerbi, Luigi, Wolpert, Daniel & Vijayakumar, Sethu.
Publication Date: 2014
Publication Information
Category: Poster
Original Language: English
2013
  Optimality under fire: Dissociating learning from Bayesian integration
Acerbi, L, Marius 't Hart, B, Behbahani, FMP & Peters, MAK 2013, 'Optimality under fire: Dissociating learning from Bayesian integration'.
In both unisensory and multisensory tasks, human observers have repeatedly been shown to be optimal or near-optimal in their integration of multiple cues (Ernst & Banks, 2002; Körding et al., 2007).
Most of the research on cue integration has assumed that the noise in each cue follows a normal distribution, and thus that (a) the variance of the noise is a perfect indicator of the reliability of the cue, and (b) optimal integration is therefore achieved via a linear combination of the cues. However, little is known about how humans might integrate other noise distributions, e.g., those that may not be symmetric or unimodal, or which may require nonlinear cue combination. Here we ask if human observers are able to learn both lower-order and higher-order statistics (e.g., skewness) of non-normal distributions, and whether and how the acquired statistical features of such distributions affect cue integration.
General Information
Organisations: Neuroinformatics DTC.
Authors: Acerbi, Luigi, Marius 't Hart, Bernard, Behbahani, Feryal M. P. & Peters, Megan A. K. .
Publication Date: Nov 2013
Publication Information
Category: Poster
Original Language: English
2012
  Internal representations of temporal statistics and feedback in sensorimotor interval timing
Acerbi, L, Wolpert, D & Vijayakumar, S 2012, 'Internal representations of temporal statistics and feedback in sensorimotor interval timing' 9th Annual Annual Computational and Systems Neurscience Meeting (COSYNE 2012), Salt Lake City, United States, 23/02/12 - 26/02/12, .
Recent results have shown that bias and variance trade-offs in time perception can be accounted for by "optimal" probabilistic inference [1]. However, specific temporal statistics of the stimuli seem to induce sub-optimal behaviours; for instance adaptor distributions, in which one inter-stimulus duration appears overwhelmingly often, typically cause a temporal recalibration effect [2] that defies a simple account based on prior expectations.

The Bayesian ideal observer responses depend crucially on both the internal representation of the temporal context (subjective prior and likelihoods) and on the loss function; observed "sub-optimal" behaviours could be caused by a systematic mismatch between the objective statistics of the experiment and their subjective counterparts. When, how and the degree to which people can learn a correct internal representation of the temporal context can be revealing of the underlying mechanisms. In this work, we studied how internal representations of temporal statistics are affected by uniform and adaptor distributions of action-stimulus intervals in a time interval reproduction paradigm. By providing different shapes of performance feedback (i.e. loss functions) to the subjects (see Methods), we also investigated how the participants integrated external error signals with the temporal context.

Our results show that temporal context calibrates sensorimotor timing according to the "scalar property" of sensorimotor error on short/long intervals in the subsecond range. The subjects typically learnt smoothed approximations of the experimental distributions of stimuli, with a good estimate of their mean and variance but also took into account higher-order statistics. The responses were sensitive to the nature of the feedback provided, in general agreement with the behaviour predicted by the related loss function. Interestingly, the above results also held in the adaptor condition, implying that there are no significant limitations in learning complex temporal distributions of stimuli with the help of corrective feedback.

[1] Jazayeri, M. and Shadlen, M.N. "Temporal context calibrates interval timing"?. Nat. Neurosci 13, 8, 1020-1026 (2010).
[2] Stetson, C. et al. "Motor-sensory recalibration leads to an illusory reversal of action and sensation". Neuron 51, 5, 651-659 (2006).
General Information
Organisations: Institute of Perception, Action and Behaviour .
Authors: Acerbi, Luigi, Wolpert, Daniel & Vijayakumar, Sethu.
Publication Date: 2012
Publication Information
Category: Poster
Original Language: English
  Internal Representations of Temporal Statistics and Feedback Calibrate Motor-Sensory Interval Timing
Acerbi, L, Wolpert, D & Vijayakumar, S 2012, 'Internal Representations of Temporal Statistics and Feedback Calibrate Motor-Sensory Interval Timing' PLoS Computational Biology, vol 8, no. 11, e1002771. DOI: 10.1371/journal.pcbi.1002771

Human performance in a timing task depends on the context of recently experienced time intervals. In fact, people may use prior experience to improve their timing performance. Given the relevance of time for both sensing and acting in the world, how humans learn and represent temporal information is a fundamental question in neuroscience. Here, we ask subjects to reproduce the duration of time intervals drawn from different distributions (different temporal contexts). We build a set of models of how people might behave in such a timing task, depending on how they are representing the temporal context. Comparison between models and data allows us to establish that in general subjects are integrating task-relevant temporal information with the provided error feedback to enhance their timing performance. Analysis of the subjects' responses allows us to reconstruct their internal representation of the temporal context, and we compare it with the true distribution. We find that with the help of corrective feedback humans can learn good approximations of unimodal distributions of time intervals used in the experiment, even for skewed distributions of durations; on the other hand, under similar conditions, we find that multimodal distributions of timing intervals are much harder to acquire.


General Information
Organisations: Institute of Perception, Action and Behaviour .
Authors: Acerbi, Luigi, Wolpert, Daniel & Vijayakumar, Sethu.
Publication Date: 1 Nov 2012
Publication Information
Category: Article
Journal: PLoS Computational Biology
Volume: 8
Issue number: 11
Original Language: English
DOIs: 10.1371/journal.pcbi.1002771
2011
  Bayesian causal inference drives temporal sensorimotor recalibration
Acerbi, L & Vijayakumar, S 2011, 'Bayesian causal inference drives temporal sensorimotor recalibration'.
How does the brain evaluate and represent the time interval between a sensorimotor pair of events like a button press and a flash? Psychophysical experiments have shown that the relative position in time of the two events is subject to contraction (causal/intentional binding) and to adaptive shifts which lead to striking time-ordering reversal illusions (temporal recalibration). The subjective structure and representation of time appears, hence, to be extremely fluid and nonlinear. In this work, we hypothesize that these phenomena are a consequence of Bayesian causal structural inference and propose a compact generative modelling approach.

Specifically, causal binding can be interpreted as an (attractive) prior between potentially related events, while temporal recalibration follows from the inference of the temporal onset between the visual and motor feedback (due to transmission delays, processing times, etc.). In particular, a Bayesian observer should exhibit recalibration to a sensory lag only if two crossmodal sensory events are thought to be causally related - and thus most likely simultaneous; the likelihood of which we propose is driven by a model selection paradigm.

The proposed model obtains excellent fits - as good as the best known empirical fit [2], to psychophysical data of temporal recalibration experiments from different modalities and with various delays between the button press and stimuli. More importantly, having estimated some subject specific parameters, we were able to make predictions about the effect of noisy adaptation stimuli on recalibration with good quantitative match - as expected, temporal recalibration is modulated by stimulus temporal reliability.

As a further validation, the sensory parameters obtained by fitting the model to the recalibration data correlated extremely well with those measured in an independent experiment (a time interval discrimination task), implying the model can reliably recover those parameters.

This work presents the first attempts at generative modeling of time interval estimation in a sensorimotor task that goes beyond empirical fitting and provides new ways to investigate departures from the "scalar property" of interval estimation in the subsecond range. This also provides preliminary evidence that several recalibration and fast adaptation phenomena in the temporal domain can be explained as a consequence of optimal Bayesian structural inference that our brain may be inferring about.
General Information
Organisations: Institute of Perception, Action and Behaviour .
Authors: Acerbi, Luigi & Vijayakumar, S..
Keywords: (Inferring the structure of space-time through action and perception. )
Publication Date: 2011
Publication Information
Category: Poster
Original Language: English

Projects:
Inferring the structure of space-time through action and perception (PhD)