Related papers: Determining classes for generalized $\psi$-estimat…
We propose a general class of sample based explanations of machine learning models, which we term generalized representers. To measure the effect of a training sample on a model's test prediction, generalized representers use two…
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
In a completely randomized experiment, the variances of treatment effect estimators in the finite population are usually not identifiable and hence not estimable. Although some estimable bounds of the variances have been established in the…
In order to study the analytic properties of the Goldbach generating function we consider a smooth version, similar to the Chebyshev function for the Prime Number Theorem. In this paper, we obtain explicit numerical estimates for the…
In this paper, we consider statistical inference with generalized linear models in high dimensions under a longitudinal clustered data framework. Specifically, we propose a de-sparsified version of an initial Dantzig-type regularized…
If $G$ is a finite classical group, linear or unitary in any characteristic, and orthogonal in odd characteristic, we give an approximate formula for $\chi(g)$ in which the error term is much smaller than the estimate, when $g\in G$ is an…
We introduce unbiased estimators for the Shannon entropy and the class number, in the situation that we are able to take sequences of independent samples of arbitrary length.
Binary observations are often repeated to improve data quality, creating technical replicates. Several scoring methods are commonly used to infer the actual individual state and obtain a probability for each state. The common practice of…
Tsallis has suggested a nonextensive generalization of the Boltzmann-Gibbs entropy, the maximization of which gives a generalized canonical distribution under special constraints. In this brief report we show that the generalized canonical…
The entailment problem $\varphi \models \psi$ in Separation Logic \cite{IshtiaqOHearn01,Reynolds02}, between separated conjunctions of equational ($x \iseq y$ and $x \not\iseq y$), spatial ($x \mapsto (y_1,\ldots,y_\rank)$) and predicate…
The naive importance sampling estimator, based on samples from a single importance density, can be numerically unstable. Instead, we consider generalized importance sampling estimators where samples from more than one probability…
Our interest is whether two binomial parameters differ, which parameter is larger, and by how much. This apparently simple problem was addressed by Fisher in the 1930's, and has been the subject of many review papers since then. Yet there…
Two years ago, Conlon and Gowers, and Schacht proved general theorems that allow one to transfer a large class of extremal combinatorial results from the deterministic to the probabilistic setting. Even though the two papers solve the same…
A common goal in statistics and machine learning is estimation of unknowns. Point estimates alone are of little value without an accompanying measure of uncertainty, but traditional uncertainty quantification methods, such as confidence…
We obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result…
Shannon defined the mutual information between two variables. We illustrate why the true mutual information between a variable and the predictions made by a prediction algorithm is not a suitable measure of prediction quality, but the…
We obtain a formula which reduces the evaluation of a $_2\psi_2$ series to two $_2\phi_1$ series. In some sense, this identity may be considered as a companion of Slater's formulas. We also find that a two-term ${}_2\psi_2$ summation…
A class of discrete probability distributions contains distributions with limited support, i.e. possible argument values are limited to a set of numbers (typically consecutive). Examples of such data are results from subjective experiments…
An accurate multiclass classification strategy is crucial to interpreting antibody tests. However, traditional methods based on confidence intervals or receiver operating characteristics lack clear extensions to settings with more than two…