Related papers: Measure Theory and Integration By and For the Lear…
Active learning comprises many varied techniques that engage students actively in the construction of their understanding. Because of this variation, different active learning techniques may be best suited to achieving different learning…
This monograph offers a toolbox of mathematical techniques, which have been effective and widely applicable in information-theoretic analysis. The first tool is a generalization of the method of types to Gaussian settings, and then to…
This work presents a systematic study of objective evaluations of abstaining classifications using Information-Theoretic Measures (ITMs). First, we define objective measures for which they do not depend on any free parameter. This…
This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby…
The objective of physics laboratory training is to develop, in students, a variety of important cognitive and psycho-motor abilities related to experimental physics. These include conceptual understanding, procedural understanding,…
As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently…
The ``Painlev\'e analysis'' is quite often perceived as a collection of tricks reserved to experts. The aim of this course is to demonstrate the contrary and to unveil the simplicity and the beauty of a subject which is in fact the theory…
Models often need to be constrained to a certain size for them to be considered interpretable. For example, a decision tree of depth 5 is much easier to understand than one of depth 50. Limiting model size, however, often reduces accuracy.…
We present ir-measures, a new tool that makes it convenient to calculate a diverse set of evaluation measures used in information retrieval. Rather than implementing its own measure calculations, ir-measures provides a common interface to a…
During the last two decades, concentration inequalities have been the subject of exciting developments in various areas, including convex geometry, functional analysis, statistical physics, high-dimensional statistics, pure and applied…
The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…
In this paper we consider the axiomatic characterization of information and certainty measures in a unified way. We present the general axiomatic system which captures the common properties of a large number of the measures previously…
Automatically evaluating the coherence of summaries is of great significance both to enable cost-efficient summarizer evaluation and as a tool for improving coherence by selecting high-scoring candidate summaries. While many different…
The increasing practice of engaging crowds, where organizations use IT to connect with dispersed individuals for explicit resource creation purposes, has precipitated the need to measure the precise processes and benefits of these…
We present a scantron-based survey which examines the teacher-learner collaboration. The survey includes questions which probe student preparedness, behaviors, attitudes, and expectations - as well as questions addressing key measures of…
In his 1918 paper 'A General Form of Integral', Percy John Daniell developed a theory of integration capable of dealing with functions on arbitrary sets. Daniell's method differs from the measure-theoretic notion of integration. Linear…
Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…
People learn whenever and wherever possible, and whatever they like or encounter--Mathematics, Drama, Art, Languages, Physics, Philosophy, and so on. With the bursting of knowledge, evaluation of one's possession of knowledge becomes…
Existing work on understanding deep learning often employs measures that compress all data-dependent information into a few numbers. In this work, we adopt a perspective based on the role of individual examples. We introduce a measure of…
We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to…