Related papers: Optimal Direct Sum Results for Deterministic and R…
A rich mathematical structure underlying flavor sum rules has been discovered recently. In this work, we extend these findings to systems with a direct sum of representations. We prove several results for the general case. We derive an…
We consider finding a counterfactual explanation for a classification or regression forest, such as a random forest. This requires solving an optimization problem to find the closest input instance to a given instance for which the forest…
This work is related to the implementation of a decision tree construction algorithm on a quantum simulator. Here we consider an algorithm based on a binary criterion. Also, we study the improvement capability with quantum heuristic QAOA.…
We prove that some exact geometric pattern matching problems reduce in linear time to $k$-SUM when the pattern has a fixed size $k$. This holds in the real RAM model for searching for a similar copy of a set of $k\geq 3$ points within a set…
The automatic generation of decision trees based on off-line reasoning on models of a domain is a reasonable compromise between the advantages of using a model-based approach in technical domains and the constraints imposed by embedded…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…
In communication complexity the input of a function $f:X\times Y\rightarrow Z$ is distributed between two players Alice and Bob. If Alice knows only $x\in X$ and Bob only $y\in Y$, how much information must Alice and Bob share to be able to…
In this work, we provide a fundamental unified convergence theorem used for deriving expected and almost sure convergence results for a series of stochastic optimization methods. Our unified theorem only requires to verify several…
We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…
We study the model-checking problem for recursion schemes: does the tree generated by a given higher-order recursion scheme satisfy a given logical sentence. The problem is known to be decidable for sentences of the MSO logic. We prove…
Complexity theory offers a variety of concise computational models for computing boolean functions - branching programs, circuits, decision trees and ordered binary decision diagrams to name a few. A natural question that arises in this…
The optimization version of the cavity method for single instances, called Max-Sum, has been applied in the past to the Minimum Steiner Tree Problem on Graphs and variants. Max-Sum has been shown experimentally to give asymptotically…
We propose a new conjecture on some exponential sums. These particular sums have not apparently been considered in the literature. Subject to the conjecture we obtain the first effective construction of asymptotically good tree codes. The…
Automatic numerical algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. The computational cost is often determined \emph{adaptively} by the algorithm based…
Systems of decision rules and decision trees are widely used as a means for knowledge representation, as classifiers, and as algorithms. They are among the most interpretable models for classifying and representing knowledge. The study of…
Consider a collection of weighted subsets of a ground set N. Given a query subset Q of N, how fast can one (1) find the weighted sum over all subsets of Q, and (2) sample a subset of Q proportionally to the weights? We present a tree-based…
Decision trees are ubiquitous in machine learning for their ease of use and interpretability. Yet, these models are not typically employed in reinforcement learning as they cannot be updated online via stochastic gradient descent. We…
We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new…
A determined algorithm is presented for solving the rSUM problem for any natural r with a sub-quadratic assessment of time complexity in some cases. In terms of an amount of memory used the obtained algorithm is the nlog^3(n) order. The…
Inferring a decision tree from a given dataset is one of the classic problems in machine learning. This problem consists of buildings, from a labelled dataset, a tree such that each node corresponds to a class and a path between the tree…