Related papers: All Sampling Methods Produce Outliers
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
Probabilistic programming languages allow programmers to write down conditional probability distributions that represent statistical and machine learning models as programs that use observe statements. These programs are run by accumulating…
A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…
We show that it is impossible to prove that the outcome of a quantum measurement is random.
Probability models are only useful at explaining the uncertainty of what we do not know, and should never be used to say what we already know. Probability and statistical models are useless at discerning cause. Classical statistical…
Unlike Martin-L\"of randomness and Schnorr randomness, computable randomness has not been defined, except for a few ad hoc cases, outside of Cantor space. This paper offers such a definition (actually, several equivalent definitions), and…
Probabilistic programming languages rely fundamentally on some notion of sampling, and this is doubly true for probabilistic programming languages which perform Bayesian inference using Monte Carlo techniques. Verifying samplers - proving…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
Z-scores are often employed in outlier detection in a dataset. For small samples, the presence of multiple outliers forces a finite supremum on the absolute value of possible z-scores that decreases with an increasing number of outliers,…
Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier…
How to generate provably true randomness with minimal assumptions? This question is important not only for the efficiency and the security of information processing, but also for understanding how extremely unpredictable events are possible…
Works, briefly surveyed here, are concerned with two basic methods: Maximum Probability and Bayesian Maximum Probability; as well as with their asymptotic instances: Relative Entropy Maximization and Maximum Non-parametric Likelihood.…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
Clustering has many important applications in computer science, but real-world datasets often contain outliers. Moreover, the presence of outliers can make the clustering problems to be much more challenging. To reduce the complexities,…
We consider the product of infinitely many copies of a spin-$1\over 2$ system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of $\sigma^x$…
We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision…
Monte Carlo methods, Variational Inference, and their combinations play a pivotal role in sampling from intractable probability distributions. However, current studies lack a unified evaluation framework, relying on disparate performance…
The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…