Konrad P. Körding

Bayesian integration in sensorimotor learning

When we learn a new motor skill, such as playing an approaching tennis ball, both our sensors and the task possess variability. Our sensors provide imperfect information about the balls velocity, so we can only estimate it. Combining information from multiple modalities can reduce the error in this estimate. On a longer time scale, not all velocities are a priori equally probable, and over the course of a match there will be a probability distribution of velocities. According to bayesian theory, an optimal estimate results from combining information about the distribution of velocities—the prior—with evidence from sensory feedback. As uncertainty increases, when playing in fog or at dusk, the system should increasingly rely on prior knowledge. To use a bayesian strategy, the brain would need to represent the prior distribution and the level of uncertainty in the sensory feedback. Here we control the statistical variations of a new sensorimotor task and manipulate the uncertainty of the sensory feedback. We show that subjects internally represent both the statistical distribution of the task and their sensory uncertainty, combining them in a manner consistent with a performance-optimizing bayesian process. The central nervous system therefore employs probabilistic models during sensorimotor learning.

Bayesian decision theory in sensorimotor control.

Action selection is a fundamental decision process for us, and depends on the state of both our body and the environment. Because signals in our sensory and motor systems are corrupted by variability or noise, the nervous system needs to estimate these states. To select an optimal action these state estimates need to be combined with knowledge of the potential costs or rewards of different action outcomes. We review recent studies that have investigated the mechanisms used by the nervous system to solve such estimation and decision problems, which show that human behaviour is close to that predicted by Bayesian Decision Theory. This theory defines optimal behaviour in a world characterized by uncertainty, and provides a coherent way of describing sensorimotor processes.

Causal Inference in Multisensory Perception

Perceptual events derive their significance to an animal from their meaning about the world, that is from the information they carry about their causes. The brain should thus be able to efficiently infer the causes underlying our sensory events. Here we use multisensory cue combination to study causal inference in perception. We formulate an ideal-observer model that infers whether two sensory cues originate from the same location and that also estimates their location(s). This model accurately predicts the nonlinear integration of cues by human subjects in two auditory-visual localization tasks. The results show that indeed humans can efficiently infer the causal structure as well as the location of causes. By combining insights from the study of causal inference with the ideal-observer approach to sensory cue combination, we show that the capacity to infer causal structure is not limited to conscious, high-level cognition; it is also performed continually and effortlessly in perception.

The dynamics of memory as a consequence of optimal adaptation to a changing body.

There are many causes for variation in the responses of the motor apparatus to neural commands. Fast-timescale disturbances occur when muscles fatigue. Slow-timescale disturbances occur when muscles are damaged or when limb dynamics change as a result of development. To maintain performance, motor commands need to adapt. Computing the best adaptation in response to any performance error results in a credit assignment problem: which timescale is responsible for this disturbance? Here we show that a Bayesian solution to this problem accounts for numerous behaviors of animals during both short- and long-term training. Our analysis focused on characteristics of the oculomotor system during learning, including the effects of time passage. However, we suggest that learning and memory in other paradigms, such as reach adaptation, adaptation of visual neurons and retrieval of declarative memories, largely follow similar rules.

How advances in neural recording affect data analysis

Over the last five decades, progress in neural recording techniques has allowed the number of simultaneously recorded neurons to double approximately every 7 years, mimicking Moores law. Such exponential growth motivates us to ask how data analysis techniques are affected by progressively larger numbers of recorded neurons. Traditionally, neurons are analyzed independently on the basis of their tuning to stimuli or movement. Although tuning curve approaches are unaffected by growing numbers of simultaneously recorded neurons, newly developed techniques that analyze interactions between neurons become more accurate and more complex as the number of recorded neurons increases. Emerging data analysis techniques should consider both the computational costs and the potential for more accurate models associated with this exponential growth of the number of recorded neurons.

Relevance of error: what drives motor adaptation?

During motor adaptation the nervous system constantly uses error information to improve future movements. Todays mainstream models simply assume that the nervous system adapts linearly and proportionally to errors. However, not all movement errors are relevant to our own action. The environment may transiently disturb the movement production-for example, a gust of wind blows the tennis ball away from its intended trajectory. Apparently the nervous system should not adapt its motor plan in the subsequent tennis strokes based on this irrelevant movement error. We hypothesize that the nervous system estimates the relevance of each observed error and adapts strongly only to relevant errors. Here we present a Bayesian treatment of this problem. The model calculates how likely an error is relevant to the motor plant and derives an ideal adaptation strategy that leads to the most precise movements. This model predicts that adaptation should be a nonlinear function of the size of an error. In reaching experiments we found strong evidence for the predicted nonlinear strategy. The model also explains published data on saccadic gain adaptation, adaptation to visuomotor rotations, and force perturbations. Our study suggests that the nervous system constantly and effortlessly estimates the relevance of observed movement errors for successful motor adaptation.

Decision theory: what "should" the nervous system do?

The purpose of our nervous system is to allow us to successfully interact with our environment. This normative idea is formalized by decision theory that defines which choices would be most beneficial. We live in an uncertain world, and each decision may have many possible outcomes; choosing the best decision is thus complicated. Bayesian decision theory formalizes these problems in the presence of uncertainty and often provides compact models that predict observed behavior. With its elegant formalization of the problems faced by the nervous system, it promises to become a major inspiration for studies in neuroscience.

Estimating the sources of motor errors for adaptation and generalization

Motor adaptation is usually defined as the process by which our nervous system produces accurate movements while the properties of our bodies and our environment continuously change. Many experimental and theoretical studies have characterized this process by assuming that the nervous system uses internal models to compensate for motor errors. Here we extend these approaches and construct a probabilistic model that not only compensates for motor errors but estimates the sources of these errors. These estimates dictate how the nervous system should generalize. For example, estimated changes of limb properties will affect movements across the workspace but not movements with the other limb. We provide evidence that many movement-generalization phenomena emerge from a strategy by which the nervous system estimates the sources of our motor errors.

Mobile Phone Sensor Correlates of Depressive Symptom Severity in Daily-Life Behavior: An Exploratory Study

Background Depression is a common, burdensome, often recurring mental health disorder that frequently goes undetected and untreated. Mobile phones are ubiquitous and have an increasingly large complement of sensors that can potentially be useful in monitoring behavioral patterns that might be indicative of depressive symptoms. Objective The objective of this study was to explore the detection of daily-life behavioral markers using mobile phone global positioning systems (GPS) and usage sensors, and their use in identifying depressive symptom severity. Methods A total of 40 adult participants were recruited from the general community to carry a mobile phone with a sensor data acquisition app (Purple Robot) for 2 weeks. Of these participants, 28 had sufficient sensor data received to conduct analysis. At the beginning of the 2-week period, participants completed a self-reported depression survey (PHQ-9). Behavioral features were developed and extracted from GPS location and phone usage data. Results A number of features from GPS data were related to depressive symptom severity, including circadian movement (regularity in 24-hour rhythm; r=-.63, P=.005), normalized entropy (mobility between favorite locations; r=-.58, P=.012), and location variance (GPS mobility independent of location; r=-.58, P=.012). Phone usage features, usage duration, and usage frequency were also correlated (r=.54, P=.011, and r=.52, P=.015, respectively). Using the normalized entropy feature and a classifier that distinguished participants with depressive symptoms (PHQ-9 score ≥5) from those without (PHQ-9 score <5), we achieved an accuracy of 86.5%. Furthermore, a regression model that used the same feature to estimate the participants’ PHQ-9 scores obtained an average error of 23.5%. Conclusions Features extracted from mobile phone sensor data, including GPS and phone usage, provided behavioral markers that were strongly related to depressive symptom severity. While these findings must be replicated in a larger study among participants with confirmed clinical symptoms, they suggest that phone sensors offer numerous clinical opportunities, including continuous monitoring of at-risk populations with little patient burden and interventions that can provide just-in-time outreach.

The statistics of natural hand movements

Humans constantly use their hands to interact with the environment and they engage spontaneously in a wide variety of manual activities during everyday life. In contrast, laboratory-based studies of hand function have used a limited range of predefined tasks. The natural movements made by the hand during everyday life have thus received little attention. Here, we developed a portable recording device that can be worn by subjects to track movements of their right hand as they go about their daily routine outside of a laboratory setting. We analyse the kinematic data using various statistical methods. Principal component analysis of the joint angular velocities showed that the first two components were highly conserved across subjects, explained 60% of the variance and were qualitatively similar to those reported in previous studies of reach-to-grasp movements. To examine the independence of the digits, we developed a measure based on the degree to which the movements of each digit could be linearly predicted from the movements of the other four digits. Our independence measure was highly correlated with results from previous studies of the hand, including the estimated size of the digit representations in primary motor cortex and other laboratory measures of digit individuation. Specifically, the thumb was found to be the most independent of the digits and the index finger was the most independent of the fingers. These results support and extend laboratory-based studies of the human hand.