Variational Bayesian inference for linear and logistic regression

The article describe the model, derivation, and implementation of variational Bayesian inference for linear and logistic regression, both with and without automatic relevance determination. It has the dual function of acting as a tutorial for the derivation of variational Bayesian inference for simple models, as well as documenting, and providing brief examples for the MATLAB/Octave functions that implement this inference. These functions are freely available online.Comment: 28 pages, 6 figure

Optimal decision bounds for probabilistic population codes and time varying evidence

Decision making under time constraints requires the decision maker to trade off between making quick, inaccurate decisions and gathering more evidence for more accurate, but slower decisions. We have previously shown that, under rather general settings, optimal behavior can be described by a time-dependent decision bound on the decision maker’s belief of being correct (Drugowitsch, Moreno-Bote, Pouget, 2009). In cases where the reliability of sensory information remains constant over time, we have shown how to design diffusion models (DMs) with time-changing boundaries that feature such behavior. Such theories can be easily mapped onto simple neural models of decision making with two perfectly anti-correlated neurons, where they predict the existence of a stopping bound on the most active neurons. It is unclear however how the stopping bound would be implemented with more realistic neural population codes, particularly when the reliability of the evidence changes over time.
Here we show that, under certain realistic conditions, we can apply the theory of optimal decision making to the biologically more plausible probabilistic population codes (PPCs; Ma et al. 2006). Our analysis shows that, with population codes, the optimal decision bounds are a function of the neural activity of all neurons in the population, rather than a previously postulated bound on its maximum activity. This theory predicts that the bound on the most active neurons would appear to shift depending on the firing rate of other neurons in the population, a puzzling behavior under the drift diffusion model as it would wrongly suggest that subjects change their stopping rule across conditions. This theory also applies to the case of time varying evidence, a case that cannot be handled by drift diffusion models without unrealistic assumptions

Maximizing decision rate in multisensory integration

Effective decision-making in an uncertain world requires making use of all available information, even if distributed across different sensory modalities, as well as trading off the speed of a decision with its accuracy. In tasks with a fixed stimulus presentation time, animal and human subjects have previously been shown to combine information from several modalities in a statistically optimal manner. Furthermore, for easily discriminable stimuli and under the assumption that reaction times result from a race-to-threshold mechanism, multimodal reaction times are typically faster than predicted from unimodal conditions when assuming independent (parallel) races for each modality. However, due to a lack of adequate ideal observer models, it has remained unclear whether subjects perform optimal cue combination when they are allowed to choose their response times freely.
Based on data collected from human subjects performing a visual/vestibular heading discrimination task, we show that the subjects exhibit worse discrimination performance in the multimodal condition than predicted by standard cue combination criteria, which relate multimodal discrimination performance to sensitivity in the unimodal conditions. Furthermore, multimodal reaction times are slower than those predicted by a parallel race model, opposite to what is commonly observed for easily discriminable stimuli.
Despite violating the standard criteria for optimal cue combination, we show that subjects still accumulate evidence optimally across time and cues, even when the strength of the evidence varies with time. Additionally, subjects adjust their decision bounds, controlling the trade-off between speed and accuracy of a decision, such that they feature correct decision rates close to the maximum achievable value

Learning classifier systems from first principles: A probabilistic reformulation of learning classifier systems from the perspective of machine learning

Learning Classifier Systems (LCS) are a family of rule-based machine learning methods. They aim at the autonomous production of potentially human readable results that are the most compact generalised representation whilst also maintaining high predictive accuracy, with a wide range of application areas, such as autonomous robotics, economics, and multi-agent systems. Their design is mainly approached heuristically and, even though their performance is competitive in regression and classification tasks, they do not meet their expected performance in sequential decision tasks despite being initially designed for such tasks. It is out contention that improvement is hindered by a lack of theoretical understanding of their underlying mechanisms and dynamics.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Optimal policy for value-based decision-making

For decades now, normative theories of perceptual decisions, and their implementation as drift diffusion models, have driven and significantly improved our understanding of human and animal behaviour and the underlying neural processes. While similar processes seem to govern value-based decisions, we still lack the theoretical understanding of why this ought to be the case. Here, we show that, similar to perceptual decisions, drift diffusion models implement the optimal strategy for value-based decisions. Such optimal decisions require the models' decision boundaries to collapse over time, and to depend on the a priori knowledge about reward contingencies. Diffusion models only implement the optimal strategy under specific task assumptions, and cease to be optimal once we start relaxing these assumptions, by, for example, using non-linear utility functions. Our findings thus provide the much-needed theory for value-based decisions, explain the apparent similarity to perceptual decisions, and predict conditions under which this similarity should break down

Scaling of sensory information in largeneural populations shows signatures ofinformation-limiting correlations

How is information distributed across large neuronal populations within a given brain area? Information may be distributed roughly evenly across neuronal populations, so that total information scales linearly with the number of recorded neurons. Alternatively, the neural code might be highly redundant, meaning that total information saturates. Here we investigate how sensory information about the direction of a moving visual stimulus is distributed across hundreds of simultaneously recorded neurons in mouse primary visual cortex. We show that information scales sublinearly due to correlated noise in these populations. We compartmentalized noise correlations into information-limiting and nonlimiting components, then extrapolate to predict how information grows with even larger neural populations. We predict that tens of thousands of neurons encode 95% of the information about visual stimulus direction, much less than the number of neurons in primary visual cortex. These findings suggest that the brain uses a widely distributed, but nonetheless redundant code that supports recovering most sensory information from smaller subpopulations.We would like to thank Alexandre Pouget, Peter Latham, and members of the HMSNeurobiology Department for useful discussions and feedback on the work, and RachelWilson and Richard Born for comments on early versions of the manuscript. The workwas supported by a scholar award from the James S. McDonnell Foundation (grant#220020462 to J.D.), grants from the NIH (R01MH115554 to J.D.; R01MH107620 to C.D.H.; R01NS089521 to C.D.H.; R01NS108410 to C.D.H.; F31EY031562 to A.W.J.), theNSF’s NeuroNex program (DBI-1707398. to R.N.), MINECO (Spain; BFU2017-85936-Pto R.M.-B.), the Howard Hughes Medical Institute (HHMI, ref 55008742 to R.M.-B.), theICREA Academia (2016 to R.M.-B.), the Government of Aragon (Spain; ISAAC lab, codT33 17D to I.A.-R.), the Spanish Ministry of Economy and Competitiveness (TIN2016-80347-R to I.A.-R.), the Gatsby Charitable Foundation (to R.N.), and an NSF GraduateResearch Fellowship (to A.W.J.)

Of monkeys and men:Impatience in perceptual decision-making

For decades sequential sampling models have successfully accounted for human and monkey decision-making, relying on the standard assumption that decision makers maintain a pre-set decision standard throughout the decision process. Based on the theoretical argument of reward rate maximization, some authors have recently suggested that decision makers become increasingly impatient as time passes and therefore lower their decision standard. Indeed, a number of studies show that computational models with an impatience component provide a good fit to human and monkey decision behavior. However, many of these studies lack quantitative model comparisons and systematic manipulations of rewards. Moreover, the often-cited evidence from single-cell recordings is not unequivocal and complimentary data from human subjects is largely missing. We conclude that, despite some enthusiastic calls for the abandonment of the standard model, the idea of an impatience component has yet to be fully established; we suggest a number of recently developed tools that will help bring the debate to a conclusive settlement

Neuromatch Academy: a 3-week, online summer school in computational neuroscience

Neuromatch Academy (https://academy.neuromatch.io; (van Viegen et al., 2021)) was designed as an online summer school to cover the basics of computational neuroscience in three weeks. The materials cover dominant and emerging computational neuroscience tools, how they complement one another, and specifically focus on how they can help us to better understand how the brain functions. An original component of the materials is its focus on modeling choices, i.e. how do we choose the right approach, how do we build models, and how can we evaluate models to determine if they provide real (meaningful) insight. This meta-modeling component of the instructional materials asks what questions can be answered by different techniques, and how to apply them meaningfully to get insight about brain function