Probability density models based on deep networks have achieved remarkable success in modeling complex high-dimensional datasets. However, unlike kernel density estimators, modern neural models do not yield marginals or conditionals in closed form, as these quantities require the evaluation of seldom tractable integrals. In this work, we present the marginalizable density model approximator (MDMA), a novel deep network architecture which provides closed form expressions for the probabilities, marginals and conditionals of any subset of the variables. The MDMA learns deep scalar representations for each individual variable and combines them via learned hierarchical tensor decompositions into a tractable yet expressive CDF, from which marginals and conditional densities are easily obtained. We illustrate the advantage of exact marginalizability in several tasks that are out of reach of previous deep network-based density estimation models, such as estimating mutual information between arbitrary subsets of variables, inferring causality by testing for conditional independence, and inference with missing data without the need for data imputation, outperforming state-of-the-art models on these tasks. The model also allows for parallelized sampling with only a logarithmic dependence of the time complexity on the number of variables.

PARIS – MDMA, the main ingredient in ecstasy, makes humans more likely to cooperate -- but only with trustworthy people -- researchers said Monday in the first study into how the drug impacts our willingness to help others. Despite its status in Britain as a Class A drug, MDMA is widely consumed due to the heightened sense of energy, empathy and pleasure it arouses in users. It contains neurotransmitters -- chemical messengers for the brain -- that are known to be linked to behavior and mood, but scientists currently understand very little about how these affect social interactions. Researchers at King's College London studied 20 healthy adult men who were given a typical recreational dose of MDMA or a placebo pill and then asked to complete a set of tasks while images of their brain activity were taken with an MRI scanner. One of the mind exercises they were given was the Prisoner's Dilemma -- an example of so-called game theory in which an individual is asked to choose between cooperating or competing with another, unknown person.

A chemical responsible for the'loved-up' effects of the party drug ecstasy promotes teamwork but not gullibility, research suggests. Scientists found that MDMA, the drug's main active ingredient, made people better cooperators - but only when they trusted one another. They suggest that MDMA fires up parts of the brain involved in understanding the thoughts, beliefs and intentions of other people. The find could help researchers looking to treat psychological conditions such as PTSD, scientists said. Experts took brain scans of people on MDMA.

Gül Dölen and Eric Edsinger are probably the only people in the world who've watched an octopus have a bad ecstasy trip. "The first couple of animals we tried, we gave them way, way, way too much," says Dölen, a neuroscientist at John Hopkins University, "because I thought, 'well, if it's going to work it's probably going to need monster doses to see anything.'" The masters of disguise sent waves of color rippling down their arms, blanched white, and changed their breathing patterns. Suspecting that the ecstasy--also known as MDMA--was overwhelming the animals, Dölen and Edsinger, a marine biologist at the University of Chicago, dialed down the dosage. Three test trials later, they settled on one one-thousandth of the original as a reasonable amount.