Methods of Obtaining Probability Distributions

Methods of Data Analysis Learning probability distributions

One of the key problems in non-parametric data analysis is to infer good models of probability distributions, assuming we are given as data a finite sample from that distribution. This problem is ill-posed for continuous distributions, even when they are low-dimensional: with finite data, there is no way to distinguish between (or exclude) distributions that are not regularized a priori, for ex...

A Comparison of Aggregation Methods of Subjective Probability Distributions By

Methods of Data Analysis Working with probability distributions

One of the key problems in non-parametric data analysis is to create a good model of a generating probability distribution, assuming we are given as data a finite sample from that distribution. Obviously this problem is ill-posed for continuous distributions: with finite data, there is no way to distinguish between (or exclude) distributions that are not restricted to be smooth. The question th...

Conflations of Probability Distributions

The conflation of a finite number of probability distributions P1, . . . , Pn is a consolidation of those distributions into a single probability distribution Q = Q(P1, . . . , Pn), where intuitively Q is the conditional distribution of independent random variables X1, . . . ,Xn with distributions P1, . . . , Pn, respectively, given that X1 = · · · = Xn. Thus, in large classes of distributions ...

Approximability of Probability Distributions

We consider the question of how well a given distribution can be approximated with probabilistic graphical models. We introduce a new parameter, effective treewidth, that captures the degree of approximability as a tradeoff between the accuracy and the complexity of approximation. We present a simple approach to analyzing achievable tradeoffs that exploits the threshold behavior of monotone gra...