The power of placebos has long been recognized for improving numerous medical conditions such as Parkinson’s disease (PD). Little is known, however, about the mechanism underlying the placebo effect. Using the ability of endogenous dopamine to compete for [C]raclopride binding as measured by positron emission tomography, we provide in vivo evidence for substantial release of endogenous dopamine...

Expectation propagation (EP) is a deterministic approximation algorithm that is often used to perform approximate Bayesian parameter learning. EP approximates the full intractable posterior distribution through a set of local approximations that are iteratively refined for each datapoint. EP can offer analytic and computational advantages over other approximations, such as Variational Inference...

We present Fitness Expectation Maximization (FEM), a novel method for performing ‘black box’ function optimization. FEM searches the fitness landscape of an objective function using an instantiation of the well-known Expectation Maximization algorithm, producing search points to match the sample distribution weighted according to higher expected fitness. FEM updates both candidate solution para...

While all psychologically competent persons know that they will one day die, this knowledge is typically held at a distance, not fully assimilated. That is, while we do not doubt that we will die, there is another sense in which we cannot fully believe it either. However, on some rare occasions, we can grasp the reality of our mortal nature in a way that is seemingly revelatory, as if the fact ...

The Desire-as-Belief thesis (DAB) states that a rational person desires a proposition exactly to the degree that she believes or expects the proposition to be good. Many people take David Lewis to have shown the thesis to be inconsistent with Bayesian decision theory. However, as we show, Lewis’ argument was based on an Invariance condition that itself is inconsistent with the (standard formula...

So far, we discussed clustering algorithms that involve a hard assignment of each datapoint to a cluster, typically based on its proximity to other points in that cluster. However, simply assigning points to the nearest cluster is not always adequate to capture more complex structure. For example, the lecture slides show an example where one cluster is much larger and less dense than another. W...

These notes are intended to introduce concentration inequalities for martingales with bounded increments. The final section also provides a gentle introduction to conditional expectation based on sigma fields. In contrast to providing a firm foundation for measure-theoretic probability, the primary goal is to introduce the language and intuition used in the study of martingales. The presentatio...

We propose a novel framework for deriving approximations for intractable probabilistic models. This framework is based on a free energy (negative log marginal likelihood) and can be seen as a generalization of adaptive TAP [1-3] and expectation propagation (EP) [4,5] The free energy is constructed from two approximating distributions which encode different aspects of the intractable model such ...

We investigate the problem of approximate Bayesian inference for a general class of observation models by means of the expectation propagation (EP) framework for large systems under some statistical assumptions. Our approach tries to overcome the numerical bottleneck of EP caused by the inversion of large matrices. Assuming that the measurement matrices are realizations of specific types of ens...