Kant said: there are two a priori intuitions — space and time. There are also categories, and “the number of the categories in each class is always the same, namely, three”, like unity-plurality-modality, or possibility-existence-necessity. It would be fun to have three a priori intuitions, but only two exist, sigh. Really though?
Kant probably did not realize: there is a third one — probability, to wit, certainty of our experience. Just like space, probability precedes any experience. Every object is uncertain as much as it is extended.
The three a priori intuitions are related — infinite and undirected space, infinite and directed time, finite and undirected probability. Physics knows of uncertainty principle, we are uncertain about relation of time and space: both time and space cannot be intuited with certainty. Probability is as basic and fundamental as time and space for our cognition.
Just like geometry deals with a priori intuition of space, and mathematical analysis — with intuition of time, theory of probability deals with intuition of probability. There is philosophical justification for studying uncertainty, probability, and bayesian inference.
Paper, slides, and poster as presented at SOCS 2015.
We introduce an approximate search algorithm for fast maximum a posteriori probability estimation in probabilistic programs, which we call Bayesian ascent Monte Carlo (BaMC). (more…)
An early workshop paper, superseded by current research but still relevant, slides, and a poster.
We introduce a new approach to solving path-finding problems under uncertainty by representing them as probabilistic models and applying domain-independent inference algorithms to the models. (more…)
Found my own slides from a talk I gave a year ago, about rational meta-reasoning. Do they seem interesting to me because I have degraded during this year?
We introduce a new algorithm for multi-agent path finding, derived from the idea of meta-agent conflict-based search (MA-CBS). (more…)
Another poster in S5/HTML.
A good design is approximately optimal. When a reasonable probabilistic model is available, the design can be optimized in expectation: flight delays should be rare, e-mails should arrive within seconds, and buildings should protect from elements and provide comfort on most days of the year. But a single disaster can cause big trouble.