Related papers: Monotone rearrangement in averaging classes

The amount of training-data is one of the key factors which determines the generalization capacity of learning algorithms. Intuitively, one expects the error rate to decrease as the amount of training-data increases. Perhaps surprisingly,…

Quite unexpectedly, kinetic theory is found to specify the correct definition of average value to be employed in nonextensive statistical mechanics. It is shown that the normal average is consistent with the generalized Stosszahlansatz…

Monotonicity and recursivity are central assumptions in intertemporal consumption problems under ambiguity. We show that monotone recursive preferences admit both a recursive and an ex-ante representation, and that the certainty equivalent…

We study sub-semigroups of the semigroup of probability measures on $\mathbb{R}$ and monotone additive statistics on them, by which we mean maps to the reals that are monotone with respect to the stochastic order and additive under…

We propose a batchwise monotone algorithm for dictionary learning. Unlike the state-of-the-art dictionary learning algorithms which impose sparsity constraints on a sample-by-sample basis, we instead treat the samples as a batch, and impose…

We consider the extent to which we can learn from a completely randomized experiment whether all individuals have treatment effects that are weakly of the same sign, a condition we call monotonicity. From a classical sampling perspective,…

A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…

We construct bisymmetric, strictly increasing binary operations on real intervals which are not continuous. This answers a natural question in the theory of bisymmetric and mean-type operations by showing that continuity may fail for…

Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as similar (but strictly larger) classes obtained by adding articulation points to any or all of the other patterns. The method of proof is to show…

We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the…

In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of statistical functionals, aside from their large sample properties. We study such behavior in terms of…

We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the…

We give a complete list of the Lebesgue-Jordan decomposition of Boolean and monotone stable distributions and a complete list of the mode of them. They are not always unimodal.

Real-world machine learning applications may require functions that are fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for…

We generalize Monge property of real matrices for interval matrices. We define two classes of interval matrices with Monge property - in a strong and in a weak sense. We study fundamental properties of both classes. We show several…

Measuring association, or the lack of it, between variables plays an important role in a variety of research areas, including education, which is of our primary interest in this paper. Given, for example, student marks on several study…

Compositional generalization is the ability to generalize systematically to a new data distribution by combining known components. Although humans seem to have a great ability to generalize compositionally, state-of-the-art neural models…

A permutation of the integers avoiding monotone arithmetic progressions of length $6$ was constructed in (Geneson, 2018). We improve on this by constructing a permutation of the integers avoiding monotone arithmetic progressions of length…

Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…

In a multi-index model with $k$ index vectors, the input variables are transformed by taking inner products with the index vectors. A transfer function $f: \mathbb{R}^k \to \mathbb{R}$ is applied to these inner products to generate the…