On the Sensitivity Conjecture for Disjunctive Normal Forms

The sensitivity conjecture of Nisan and Szegedy [CC\u2794] asks whether for any Boolean function f, the maximum sensitivity s(f), is polynomially related to its block sensitivity bs(f), and hence to other major complexity measures. Despite major advances in the analysis of Boolean functions over the last decade, the problem remains widely open. In this paper, we consider a restriction on the class of Boolean functions through a model of computation (DNF), and refer to the functions adhering to this restriction as admitting the Normalized Block property. We prove that for any function f admitting the Normalized Block property, bs(f) <= 4 * s(f)^2. We note that (almost) all the functions mentioned in literature that achieve a quadratic separation between sensitivity and block sensitivity admit the Normalized Block property. Recently, Gopalan et al. [ITCS\u2716] showed that every Boolean function f is uniquely specified by its values on a Hamming ball of radius at most 2 * s(f). We extend this result and also construct examples of Boolean functions which provide the matching lower bounds

Using data-driven rules to predict mortality in severe community acquired pneumonia

Prediction of patient-centered outcomes in hospitals is useful for performance benchmarking, resource allocation, and guidance regarding active treatment and withdrawal of care. Yet, their use by clinicians is limited by the complexity of available tools and amount of data required. We propose to use Disjunctive Normal Forms as a novel approach to predict hospital and 90-day mortality from instance-based patient data, comprising demographic, genetic, and physiologic information in a large cohort of patients admitted with severe community acquired pneumonia. We develop two algorithms to efficiently learn Disjunctive Normal Forms, which yield easy-to-interpret rules that explicitly map data to the outcome of interest. Disjunctive Normal Forms achieve higher prediction performance quality compared to a set of state-of-the-art machine learning models, and unveils insights unavailable with standard methods. Disjunctive Normal Forms constitute an intuitive set of prediction rules that could be easily implemented to predict outcomes and guide criteria-based clinical decision making and clinical trial execution, and thus of greater practical usefulness than currently available prediction tools. The Java implementation of the tool JavaDNF will be publicly available. © 2014 Wu et al

Against Minimalist Responses to Moral Debunking Arguments

Moral debunking arguments are meant to show that, by realist lights, moral beliefs are not explained by moral facts, which in turn is meant to show that they lack some significant counterfactual connection to the moral facts (e.g., safety, sensitivity, reliability). The dominant, “minimalist” response to the arguments—sometimes defended under the heading of “third-factors” or “pre-established harmonies”—involves affirming that moral beliefs enjoy the relevant counterfactual connection while granting that these beliefs are not explained by the moral facts. We show that the minimalist gambit rests on a controversial thesis about epistemic priority: that explanatory concessions derive their epistemic import from what they reveal about counterfactual connections. We then challenge this epistemic priority thesis, which undermines the minimalist response to debunking arguments (in ethics and elsewhere)

Reasoning about Action: An Argumentation - Theoretic Approach

We present a uniform non-monotonic solution to the problems of reasoning about action on the basis of an argumentation-theoretic approach. Our theory is provably correct relative to a sensible minimisation policy introduced on top of a temporal propositional logic. Sophisticated problem domains can be formalised in our framework. As much attention of researchers in the field has been paid to the traditional and basic problems in reasoning about actions such as the frame, the qualification and the ramification problems, approaches to these problems within our formalisation lie at heart of the expositions presented in this paper

Efficiently Learning Monotone Decision Trees with ID3

Since the Probably Approximately Correct learning model was introduced in 1984, there has been much effort in designing computationally efficient algorithms for learning Boolean functions from random examples drawn from a uniform distribution. In this paper, I take the ID3 information-gain-first classification algorithm and apply it to the task of learning monotone Boolean functions from examples that are uniformly distributed over {0,1}^n. I limited my scope to the class of monotone Boolean functions that can be represented as read-2 width-2 disjunctive normal form expressions. I modeled these functions as graphs and examined each type of connected component contained in these models, i.e. path graphs and cycle graphs. I determined the influence of the variables in the pieces of these graph models in order to understand how ID3 behaves when learning these functions. My findings show that ID3 will produce an optimal decision tree for this class of Boolean functions

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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