Stochastic models of decisions about motion direction: Behavior and physiology

Abstract

Roitman and Shadlen [Roitman J. D., & Shadlen M. N. (2002). Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. Journal of Neuroscience, 22, 9475–9489] have published a non-human primate study on visual decision making. They collected both behavioral and neurophysiological data and provided evidence that the data are qualitatively consistent with a mechanism based on accumulating sensory evidence up to a decision threshold. I have previously demonstrated that a time-variant diffusion model can account quite well quantitatively for both the behavioral and the neural data. In this manuscript I discuss how well the data constrains different components and parameters of the computational process. I also discuss the biological plausibility of the model parameters. I will demonstrate that a relatively large class of models, both with and without temporal integration and both stationary and time-variant could account for the behavioral data. Both the single cell recordings from the parietal cortex and previously published data from the extrastriate visual cortex provide additional constraints. Overall, the data favor a diffusion model with time-variant gain and leaky integrators. The integration time constant, however, turns out not to be well-constrained by the data.

Introduction

Living creatures are constantly facing the problem of having to choose from a variety of possible actions. The brain has to evaluate sensory information and it has to make a decision in a way that is optimal in terms of the current goals. Psychologists have been studying such processes for a long time (see, e.g. Link (1992), Luce (1986), Ratcliff and Rouder (1998), Reddi and Carpenter (2000), Usher and McClelland (2001) and Vickers (1970)), but only recently have researchers started investigating the underlying physiological processes (see, e.g. Aminoff and Goodin (1997), Britten, Newsome, Shadlen, Celebrini, and Movshon (1996), Carpenter (1997), Glimcher (2001), Platt (2002), Reddi (2001), Romo and Salinas (2001), Schall and Bichot (1998) and Shadlen and Newsome (2001)).

In a combined behavioral and neurophysiological study of primate decision making, Roitman and Shadlen (2002) used rhesus monkeys to investigate judgments about the net direction of motion in stochastic patterns. We have previously demonstrated that both the behavioral and the physiological data (single-unit recordings from the lateral intraparietal area, LIP) are qualitatively consistent with the idea that the brain keeps accumulating sensory evidence until a critical decision threshold is reached (Mazurek, Roitman, Ditterich, & Shadlen, 2003). An abstract mathematical representation of the suggested mechanism is a bounded diffusion process. While a stationary diffusion model can account for the choice behavior and for the mean response times (RTs), it turns out to be incompatible with the observed RT distributions. I have recently shown that a time-variant diffusion model can explain the distributions of both choices and response times quantitatively. The neural responses recorded from LIP would also be consistent with such a computational mechanism. Furthermore, a time-variant decision mechanism would allow the monkey to increase its reward rate compared to a stationary one (Ditterich, 2006).

Identifying a computational mechanism that can account for a particular data set, however, does not automatically mean that it is the only one that could explain the data. In this manuscript I will therefore address the question which components and parameters of the computational process are well-constrained by the data, and which ones are not well-defined and need to be constrained by additional experiments. I will also check the biological plausibility of potential computational mechanisms by comparing estimated model parameters to known physiological properties of the involved neural structures. We will see that a relatively large class of models, both with and without temporal integration and both stationary and time-variant, turns out to be consistent with the behavioral data, including the RT distributions. However, I will demonstrate how the physiological data can help us further constrain the model properties. We will end up with evidence for a decision mechanism that can be described by a time-variant diffusion process; only the integration time constant will turn out not to be well-defined by the data set.

I will now briefly introduce the data set upon which my models are based. Details can be found in Roitman and Shadlen (2002). Fig. 1a shows the experimental task. The monkeys were allowed to watch a random dot stimulus until they were ready to respond. They reported their choice by making a saccade (fast eye movement) to one of two targets. The monkeys’ choices and RTs were measured as a function of the strength of the motion stimulus (coherence of the random dot pattern). Fig. 1b shows several aspects of the behavioral data: the monkeys’ performance was almost perfect for strong motion and declined continuously for weaker motion (left panel). The monkeys gave fast responses when presented with strong motion, but waited longer for weaker motion (right panel). On average, RTs were longer for errors compared to correct responses.

While the monkeys performed this task, single-unit activity was recorded from neurons in area LIP in the parietal cortex, which had one of the two targets in their response field (RF). Fig. 1c shows the mean firing rate as a function of time, aligned with stimulus onset. The plot shows the interval from 200 to 350 ms after stimulus onset. Different colors code for different motion strengths with solid lines indicating net motion in the direction instructing an eye movement to the target in the RF (positive motion strength) and dashed lines indicating net motion in the opposite direction (instructing an eye movement to the target outside the RF; negative motion strength). The activity stays approximately flat for pure noise stimuli (coherence of 0), ramps up for positive motion strengths, and ramps down for negative motion strengths. In the first 200 ms after stimulus onset the neurons showed a stereotyped dip and recovery in their response (independent of motion strength; see original publication). I will not attempt to replicate this feature in my models. Fig. 1d shows the activity of the LIP neurons aligned with the behavioral response (saccade onset). In this case the plot is conditionalized on the monkey’s choice: the solid traces show correct trials where the monkey chose the target in the RF, the dashed traces show correct trials where the monkey chose the target outside the RF. The plot depicts the interval from 200 to 50 ms before saccade onset. The neural responses were very similar regardless of motion strength when the monkey chose the target in the RF, and different responses were observed for different motion strengths when the monkey ended up choosing the target outside the RF. The dotted line represents the “baseline” activity after recovering from the initial dip (approx. 47 sp/s). Since neural responses occurring before the shown time interval are again “contaminated” by the initial dip in the activity they will not be used for model comparisons.