Related papers: Evaluation of DNF Formulas
Several structure learning algorithms have been proposed towards discovering causal or Bayesian Network (BN) graphs. The validity of these algorithms tends to be evaluated by assessing the relationship between the learnt and the ground…
In this paper we establish some bounds on the complexity of disjunctive normal forms of boolean function from narrow subclasses (e.g. functions takes value 0 in a limited number of points). The bounds are obtained by reduction the initial…
This paper studies the hazard-free formula complexity of Boolean functions. Our first result shows that unate functions are the only Boolean functions for which the monotone formula complexity of the hazard-derivative equals the hazard-free…
We propose novel methods for max-cost Discrete Function Evaluation Problem (DFEP) under budget constraints. We are motivated by applications such as clinical diagnosis where a patient is subjected to a sequence of (possibly expensive) tests…
Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…
This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented…
A two--step Christoffel function based solution is proposed to distribution regression problem. On the first step, to model distribution of observations inside a bag, build Christoffel function for each bag of observations. Then, on the…
Suppose that the only available information in a multi-class problem are expert estimates of the conditional probabilities of occurrence for a set of binary features. The aim is to select a subset of features to be measured in subsequent…
In stochastic contextual bandit (SCB) problems, an agent selects an action based on certain observed context to maximize the cumulative reward over iterations. Recently there have been a few studies using a deep neural network (DNN) to…
A Bayesian net (BN) is more than a succinct way to encode a probabilistic distribution; it also corresponds to a function used to answer queries. A BN can therefore be evaluated by the accuracy of the answers it returns. Many algorithms for…
When humans infer underlying probabilities from stochastic observations, they exhibit biases and variability that cannot be explained on the basis of sound, Bayesian manipulations of probability. This is especially salient when beliefs are…
The Shapley value provides a principled framework for fairly distributing rewards among participants according to their individual contributions. While prior work has applied this concept to data valuation in machine learning, existing…
Given a Boolean function $f:\{0,1\}^n\to\{0,1\}$, the goal in the usual query model is to compute $f$ on an unknown input $x \in \{0,1\}^n$ while minimizing the number of queries to $x$. One can also consider a "distinguishing" problem…
In this paper, we investigate safety-critical control problem of discrete-time stochastic systems with incomplete information, where safety constraints must be enforced using state estimates obtained from noisy measurements. We develop an…
We investigate the randomized decision tree complexity of a specific class of read-once threshold functions. A read-once threshold formula can be defined by a rooted tree, every internal node of which is labeled by a threshold function…
In constructing an econometric or statistical model, we pick relevant features or variables from many candidates. A coalitional game is set up to study the selection problem where the players are the candidates and the payoff function is a…
Machine learning models usually assume that a set of feature values used to obtain an output is fixed in advance. However, in many real-world problems, a cost is associated with measuring these features. To address the issue of reducing…
Attribution scores reflect how important the feature values in an input entity are for the output of a machine learning model. One of the most popular attribution scores is the SHAP score, which is an instantiation of the general Shapley…
In this paper we focus on the problem of assigning uncertainties to single-point predictions generated by a deterministic model that outputs a continuous variable. This problem applies to any state-of-the-art physics or engineering models…
Stochastic computation graphs (SCGs) provide a formalism to represent structured optimization problems arising in artificial intelligence, including supervised, unsupervised, and reinforcement learning. Previous work has shown that an…