Related papers: On the Impossibility of Learning the Missing Mass

The remarkable results of Foster and Vohra was a starting point for a series of papers which show that any sequence of outcomes can be learned (with no prior knowledge) using some universal randomized forecasting algorithm and…

Consider the following story: A teacher announces to her students a test for the following week, such that the test will be ``surprising''. The students use this as the basis for a ``logical derivation'' and reach a contradiction, which…

A probabilistic query may not be estimable from observed data corrupted by missing values if the data are not missing at random (MAR). It is therefore of theoretical interest and practical importance to determine in principle whether a…

Extreme events have an important role which is sometime catastrophic in a variety of natural phenomena including climate, earthquakes and turbulence, as well as in man-made environments like financial markets. Statistical analysis and…

This paper introduces a new technique for learning probabilistic models of mass and friction distributions of unknown objects, and performing robust sliding actions by using the learned models. The proposed method is executed in two…

We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under…

This paper deals with the problem of estimating the probability that one event was a cause of another in a given scenario. Using structural-semantical definitions of the probabilities of necessary or sufficient causation (or both), we show…

Machine Learning research, including work promoting fair or equitable algorithms, often relies on the concept of a data-generating probability distribution. The standard presumption is that since data points are 'sampled from' such a…

Balancing a rare and serious possibility against a more common and less serious one is a familiar problem in many situations, such as the prediction of rare diseases. The relative costs of forecasting errors can be used for any prediction…

In 2017-2020 Jordanova and co-authors investigate probabilities for p-outside values and determine them in many particular cases. They show that these probabilities are closely related to the concept for heavy tails. Tukey's boxplots are…

Statistical learning theory and the Probably Approximately Correct (PAC) criterion are the common approach to mathematical learning theory. PAC is widely used to analyze learning problems and algorithms, and have been studied thoroughly.…

We are interested in constructing concrete independent events in purely atomic probability spaces with geometric distribution. Among other facts we prove that there are uncountable many sequences of independent events.

Improving Importance Sampling estimators for rare event probabilities requires sharp approx- imations of the optimal density leading to a nearly zero-variance estimator. This paper presents a new way to handle the estimation of the…

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on…

Composite likelihoods are a class of alternatives to the full likelihood which are widely used in many situations in which the likelihood itself is intractable. A composite likelihood may be computed without the need to specify the full…

If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…

Despite the theoretical significance and wide practical use of regular expressions, the computational complexity of learning them has been largely unexplored. We study the computational hardness of improperly learning regular expressions in…

We study rare events in networks with both internal and external noise, and develop a general formalism for analyzing rare events that combines pair-quenched techniques and large-deviation theory. The probability distribution, shape, and…

In this paper, we analyze and study a hybrid model for testing and learning probability distributions. Here, in addition to samples, the testing algorithm is provided with one of two different types of oracles to the unknown distribution…

We prove an impossibility result for conditional Probably Approximately Correct (PAC)-efficient reasoning in large language models. While recent work has established marginal PAC efficiency guarantees for composite models that switch…