Jan Drugowitsch

The Cost of Accumulating Evidence in Perceptual Decision Making

Decision making often involves the accumulation of information over time, but acquiring information typically comes at a cost. Little is known about the cost incurred by animals and humans for acquiring additional information from sensory variables due, for instance, to attentional efforts. Through a novel integration of diffusion models and dynamic programming, we were able to estimate the cost of making additional observations per unit of time from two monkeys and six humans in a reaction time (RT) random-dot motion discrimination task. Surprisingly, we find that the cost is neither zero nor constant over time, but for the animals and humans features a brief period in which it is constant but increases thereafter. In addition, we show that our theory accurately matches the observed reaction time distributions for each stimulus condition, the time-dependent choice accuracy both conditional on stimulus strength and independent of it, and choice accuracy and mean reaction times as a function of stimulus strength. The theory also correctly predicts that urgency signals in the brain should be independent of the difficulty, or stimulus strength, at each trial.

Confidence and certainty: distinct probabilistic quantities for different goals.

When facing uncertainty, adaptive behavioral strategies demand that the brain performs probabilistic computations. In this probabilistic framework, the notion of certainty and confidence would appear to be closely related, so much so that it is tempting to conclude that these two concepts are one and the same. We argue that there are computational reasons to distinguish between these two concepts. Specifically, we propose that confidence should be defined as the probability that a decision or a proposition, overt or covert, is correct given the evidence, a critical quantity in complex sequential decisions. We suggest that the term certainty should be reserved to refer to the encoding of all other probability distributions over sensory and cognitive variables. We also discuss strategies for studying the neural codes for confidence and certainty and argue that clear definitions of neural codes are essential to understanding the relative contributions of various cortical areas to decision making.

Optimal multisensory decision-making in a reaction-time task

Humans and animals can integrate sensory evidence from various sources to make decisions in a statistically near-optimal manner, provided that the stimulus presentation time is fixed across trials. Little is known about whether optimality is preserved when subjects can choose when to make a decision (reaction-time task), nor when sensory inputs have time-varying reliability. Using a reaction-time version of a visual/vestibular heading discrimination task, we show that behavior is clearly sub-optimal when quantified with traditional optimality metrics that ignore reaction times. We created a computational model that accumulates evidence optimally across both cues and time, and trades off accuracy with decision speed. This model quantitatively explains subjectss choices and reaction times, supporting the hypothesis that subjects do, in fact, accumulate evidence optimally over time and across sensory modalities, even when the reaction time is under the subjects control. DOI: http://dx.doi.org/10.7554/eLife.03005.001

A formal framework and extensions for function approximation in learning classifier systems

Abstract Learning Classifier Systems (LCS) consist of the three components: function approximation, reinforcement learning, and classifier replacement. In this paper we formalize the function approximation part, by providing a clear problem definition, a formalization of the LCS function approximation architecture, and a definition of the function approximation aim. Additionally, we provide definitions of optimality and what conditions need to be fulfilled for a classifier to be optimal. As a demonstration of the usefulness of the framework, we derive commonly used algorithmic approaches that aim at reaching optimality from first principles, and introduce a new Kalman filter-based method that outperforms all currently implemented methods, in addition to providing further insight into the probabilistic basis of the localized model that a classifier provides. A global function approximation in LCS is achieved by combining the classifier’s localized model, for which we provide a simplified approach when compared to current LCS, based on the Maximum Likelihood of a combination of all classifiers. The formalizations in this paper act as the foundation of a currently actively developed formal framework that includes all three LCS components, promising a better formal understanding of current LCS and the development of better LCS algorithms.

Probabilistic vs. non-probabilistic approaches to the neurobiology of perceptual decision-making

Optimal binary perceptual decision making requires accumulation of evidence in the form of a probability distribution that specifies the probability of the choices being correct given the evidence so far. Reward rates can then be maximized by stopping the accumulation when the confidence about either option reaches a threshold. Behavioral and neuronal evidence suggests that humans and animals follow such a probabilitistic decision strategy, although its neural implementation has yet to be fully characterized. Here we show that that diffusion decision models and attractor network models provide an approximation to the optimal strategy only under certain circumstances. In particular, neither model type is sufficiently flexible to encode the reliability of both the momentary and the accumulated evidence, which is a pre-requisite to accumulate evidence of time-varying reliability. Probabilistic population codes, by contrast, can encode these quantities and, as a consequence, have the potential to implement the optimal strategy accurately.

Tuning the speed-accuracy trade-off to maximize reward rate in multisensory decision-making

For decisions made under time pressure, effective decision making based on uncertain or ambiguous evidence requires efficient accumulation of evidence over time, as well as appropriately balancing speed and accuracy, known as the speed/accuracy trade-off. For simple unimodal stimuli, previous studies have shown that human subjects set their speed/accuracy trade-off to maximize reward rate. We extend this analysis to situations in which information is provided by multiple sensory modalities. Analyzing previously collected data (Drugowitsch et al., 2014), we show that human subjects adjust their speed/accuracy trade-off to produce near-optimal reward rates. This trade-off can change rapidly across trials according to the sensory modalities involved, suggesting that it is represented by neural population codes rather than implemented by slow neuronal mechanisms such as gradual changes in synaptic weights. Furthermore, we show that deviations from the optimal speed/accuracy trade-off can be explained by assuming an incomplete gradient-based learning of these trade-offs. DOI: http://dx.doi.org/10.7554/eLife.06678.001

Computational Precision of Mental Inference as Critical Source of Human Choice Suboptimality

Making decisions in uncertain environments often requires combining multiple pieces of ambiguous information from external cues. In such conditions, human choices resemble optimal Bayesian inference, but typically show a large suboptimal variability whose origin remains poorly understood. In particular, this choice suboptimality might arise from imperfections in mental inference rather than in peripheral stages, such as sensory processing and response selection. Here, we dissociate these three sources of suboptimality in human choices based on combining multiple ambiguous cues. Using a novel quantitative approach for identifying the origin and structure of choice variability, we show that imperfections in inference alone cause a dominant fraction of suboptimal choices. Furthermore, two-thirds of this suboptimality appear to derive from the limited precision of neural computations implementing inference rather than from systematic deviations from Bayes-optimal inference. These findings set an upper bound on the accuracy and ultimate predictability of human choices in uncertain environments.

Lateral orbitofrontal cortex anticipates choices and integrates prior with current information

Adaptive behavior requires integrating prior with current information to anticipate upcoming events. Brain structures related to this computation should bring relevant signals from the recent past into the present. Here we report that rats can integrate the most recent prior information with sensory information, thereby improving behavior on a perceptual decision-making task with outcome-dependent past trial history. We find that anticipatory signals in the orbitofrontal cortex about upcoming choice increase over time and are even present before stimulus onset. These neuronal signals also represent the stimulus and relevant second-order combinations of past state variables. The encoding of choice, stimulus and second-order past state variables resides, up to movement onset, in overlapping populations. The neuronal representation of choice before stimulus onset and its build-up once the stimulus is presented suggest that orbitofrontal cortex plays a role in transforming immediate prior and stimulus information into choices using a compact state-space representation.

Causal Inference and Explaining Away in a Spiking Network

While the brain uses spiking neurons for communication, theoretical research on brain computations has mostly focused on non-spiking networks. The nature of spike-based algorithms that achieve complex computations, such as object probabilistic inference, is largely unknown. Here we demonstrate that a family of high-dimensional quadratic optimization problems with non-negativity constraints can be solved exactly and efficiently by a network of spiking neurons. The network naturally imposes the non-negativity of causal contributions that is fundamental to causal inference, and uses simple operations, such as linear synapses with realistic time constants, and neural spike generation and reset non-linearities. The network infers the set of most likely causes from an observation using explaining away, which is dynamically implemented by spike-based, tuned inhibition. The algorithm performs remarkably well even when the network intrinsically generates variable spike trains, the timing of spikes is scrambled by external sources of noise, or the network is mistuned. This type of network might underlie tasks such as odor identification and classification.

An Algorithmic Description

In the previous chapter, the optimal set of classifiers given some data \(\mathcal{D}\) was defined as the one given by the model structure \(\mathcal{M}\) that maximises \(p(\mathcal{M | D})\). In addition, a Bayesian LCS model for both regression and classification was introduced, and it was shown how to apply variational Bayesian inference to compute a lower bound on \(\ln p(\mathcal{M | D})\) for some given \(\mathcal{M}\) and \(\mathcal{D}\).