Related papers: Overdrawing Urns using Categories of Signed Probab…
Consider two urns, $A$ and $B$, where initially $A$ contains a large number $n$ of balls and $B$ is empty. At each step, with equal probability, either we pick a ball at random in $A$ and place it in $B$, or vice-versa (provided of course…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
Distributions over permutations arise in applications ranging from multi-object tracking to ranking of instances. The difficulty of dealing with these distributions is caused by the size of their domain, which is factorial in the number of…
We explore the class of exchangeable Bernoulli distributions building on their geometrical structure. Exchangeable Bernoulli probability mass functions are points in a convex polytope and we have found analytical expressions for their…
We introduce a general two colour interacting urn model on a finite directed graph, where each urn at a node, reinforces all the urns in its out-neighbours according to a fixed, non-negative and balanced reinforcement matrix. We show that…
Methods of high-dimensional probability play a central role in applications for statistics, signal processing theoretical computer science and related fields. These lectures present a sample of particularly useful tools of high-dimensional…
We give a central limit theorem, which has applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced generalized Polya urns.
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
Consider a generalized time-dependent P\'olya urn process defined as follows. Let $d\in \mathbb{N}$ be the number of urns/colors. At each time $n$, we distribute $\sigma_n$ balls randomly to the $d$ urns, proportionally to $f$, where $f$ is…
Suppose an urn contains initially any number of balls of two colours. One ball is drawn randomly and then put back with $\alpha$ balls of the same colour and $\beta$ balls of the opposite colour. Both cases, $\beta=0$ and $\beta>0$ are well…
We survey recent developments in the study of probabilistic complexity classes. While the evidence seems to support the conjecture that probabilism can be deterministically simulated with relatively low overhead, i.e., that $P=BPP$, it also…
We study an urn process with two urns, initialized with a ball each. Balls are added sequentially, the urn being chosen independently with probability proportional to the $\alpha^{th}$ power $(\alpha >1)$ of the existing number of balls. We…
Adaptive randomly reinforced urn (ARRU) is a two-color urn model where the updating process is defined by a sequence of non-negative random vectors $\{(D_{1,n}, D_{2,n});n\geq1\}$ and randomly evolving thresholds which utilize accruing…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
The histogram is an analysis tool in widespread use within many sciences, with high energy physics as a prime example. However, there exists an inherent bias in the choice of binning for the histogram, with different choices potentially…
Probability theory can be studied synthetically as the computational effect embodied by a commutative monad. In the recently proposed Markov categories, one works with an abstraction of the Kleisli category and then defines deterministic…
As observers of the universe we are physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in…
Even though probabilistic treatments of neural networks have a long history, they have not found widespread use in practice. Sampling approaches are often too slow already for simple networks. The size of the inputs and the depth of typical…