Related papers: Optimal Direct Sum Results for Deterministic and R…
For high volume data streams and large data warehouses, sampling is used for efficient approximate answers to aggregate queries over selected subsets. Mathematically, we are dealing with a set of weighted items and want to support queries…
Let $a,b\in \mathbb{N}$ be fixed and coprime such that $a>b$, and let $N$ be any number of the form $a^n\pm b^n$, $n\in\mathbb{N}$. We will generalize a result of Bostan, Gaudry and Schost and prove that we may compute the prime…
We present a definition for the sum of a sequence of combinatorial games. This sum coincides with the classical sum in the case of a converging sequence of real numbers and with the infinitary natural sum in the case of a sequence of…
This paper focuses on managing the cost of deliberation before action. In many problems, the overall quality of the solution reflects costs incurred and resources consumed in deliberation as well as the cost and benefit of execution, when…
The complete reason behind a decision is a Boolean formula that characterizes why the decision was made. This recently introduced notion has a number of applications, which include generating explanations, detecting decision bias and…
Decision trees provide a rich family of highly non-linear but efficient models, due to which they continue to be the go-to family of predictive models by practitioners across domains. But learning trees is challenging due to their discrete…
In this paper, we investigate the distribution of the maximum of partial sums of certain cubic exponential sums, commonly known as "Birch sums". Our main theorem gives upper and lower bounds (of nearly the same order of magnitude) for the…
Although many investigators affirm a desire to build reasoning systems that behave consistently with the axiomatic basis defined by probability theory and utility theory, limited resources for engineering and computation can make a complete…
We study the Helmholtz equation for a heterogeneous system in $d$ dimensions and show that it is possible to calculate exactly the sum rules of rational order using perturbation theory by relating the sum rules to suitable traces. The…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
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…
In this work, we show the first worst-case to average-case reduction for the classical $k$-SUM problem. A $k$-SUM instance is a collection of $m$ integers, and the goal of the $k$-SUM problem is to find a subset of $k$ elements that sums to…
Consider the following heuristic for building a decision tree for a function $f : \{0,1\}^n \to \{\pm 1\}$. Place the most influential variable $x_i$ of $f$ at the root, and recurse on the subfunctions $f_{x_i=0}$ and $f_{x_i=1}$ on the…
Deep neural networks have been proven powerful at processing perceptual data, such as images and audio. However for tabular data, tree-based models are more popular. A nice property of tree-based models is their natural interpretability. In…
Several real-world classification problems are example-dependent cost-sensitive in nature, where the costs due to misclassification vary between examples and not only within classes. However, standard classification methods do not take…
Nearest neighbor (kNN) methods have been gaining popularity in recent years in light of advances in hardware and efficiency of algorithms. There is a plethora of methods to choose from today, each with their own advantages and…
We study sums of a random multiplicative function; this is an example, of number-theoretic interest, of sums of products of independent random variables (chaoses). Using martingale methods, we establish a normal approximation for the sum…
Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…
Dispersive sum rules constitute long-standing tools for extracting hadron features from QCD. We estimate the systematic uncertainties induced by assuming quark-hadron duality and improve the accuracy of the resulting predictions by…
Decision-making under uncertainty is a critical aspect of many practical autonomous systems due to incomplete information. Partially Observable Markov Decision Processes (POMDPs) offer a mathematically principled framework for formulating…