Related papers: New Counterexamples for Sums-Differences
Counterfactual explanations are usually obtained by identifying the smallest change made to an input to change a prediction made by a fixed model (hereafter called sparse methods). Recent work, however, has revitalized an old insight: there…
This paper is meant as a contribution to the often debated subject of how to combine data which appear to be in mutual disagreement. As a practical example, the epsilon-prime/epsilon determinations have been considered.
In this paper we introduce a novel way to speed up the discovery of counterexamples in bounded model checking, based on parallel runs over versions of a system in which features have been randomly disabled. As shown in previous work, adding…
In recent years some near-optimal estimates have been established for certain sum-product type estimates. This paper gives some first extremal results which provide information about when these bounds may or may not be tight. The main tool…
Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…
Counterfactual explanations are attracting significant attention due to the flourishing applications of machine learning models in consequential domains. A counterfactual plan consists of multiple possibilities to modify a given instance so…
Due to the increasing use of machine learning in practice it becomes more and more important to be able to explain the prediction and behavior of machine learning models. An instance of explanations are counterfactual explanations which…
A new version of a weak nonlinear law of large numbers proposed. The existence of the first moment for any summand is not assumed. The assumption of independence is understood in the nonlinear sense, and may be further a little relaxed.
This paper deals with strong invariance principles (known also as strong approximation theorems) for sums of the form $\sum_{n=1}^{[Nt]}F\big(X(n),X(2n),...,X(kn), X(q_{k+1}(n)),X(q_{k+2}(n)),..., X(q_\ell(n))\big)$
Our aim is to give for some classes non-additive measures some limit theorems. For balanced games we obtain a weak and strong law of large numbers for bounded random variables, a sharper conclusion is obtain with exact games. We provide an…
A counter-example to lower bounds for the singular values of the sum of two matrices in [1] and [2] is given. Correct forms of the bounds are pointed out.
We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.
When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.
New cases of the multiplicity conjecture are considered.
We bound features of counterfactual choices in the nonparametric random utility model of demand, i.e. if observable choices are repeated cross-sections and one allows for unrestricted, unobserved heterogeneity. In this setting, tight bounds…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…