Related papers: Improved bounds for the randomized decision tree c…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
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…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
In the decision tree computation model for Boolean functions, the depth corresponds to query complexity, and size corresponds to storage space. The depth measure is the most well-studied one, and is known to be polynomially related to…
We study search trees with 2-way comparisons (2WCST's), which involve separate less-than and equal-to tests in their nodes, each test having two possible outcomes, yes and no. These trees have a much subtler structure than standard search…
We present a novel analysis of the expected risk of weighted majority vote in multiclass classification. The analysis takes correlation of predictions by ensemble members into account and provides a bound that is amenable to efficient…
We examine the reset threshold of randomly generated deterministic automata. We present a simple proof that an automaton with a random mapping and two random permutation letters has a reset threshold of $\mathcal{O}\big( \sqrt{n \log^3 n}…
We obtain new non-asymptotic tail bounds for the height of uniformly random trees with a given degree sequence, simply generated trees and conditioned Bienaym\'e trees (the family trees of branching processes), in the process settling three…
We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional "doubling events" when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the…
We give a new complexity bound for calculating the complex dimension of an algebraic set. Our algorithm is completely deterministic and approaches the best recent randomized complexity bounds. We also present some new, significantly sharper…
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
We are interested in computing the treewidth $\tw(G)$ of a given graph $G$. Our approach is to design heuristic algorithms for computing a sequence of improving upper bounds and a sequence of improving lower bounds, which would hopefully…
Tree-structured LSTM is promising way to consider long-distance interaction over hierarchies. However, there have been few research efforts on the hyperparameter tuning of the construction and traversal of tree-structured LSTM. To name a…
Existing guarantees in terms of rigorous upper bounds on the generalization error for the original random forest algorithm, one of the most frequently used machine learning methods, are unsatisfying. We discuss and evaluate various…
We show that if k-SUM is hard, in the sense that the standard algorithm is essentially optimal, then a variant of the SETH called the Primal Treewidth SETH is true. Formally: if there is an $\varepsilon>0$ and an algorithm which solves SAT…
In this work, we present an $\Omega\left(\min\{\log \Delta, \sqrt{\log n}\}\right)$ lower bound for Maximal Matching (MM) in $\Delta$-ary trees against randomized algorithms. By a folklore reduction, the same lower bound applies to Maximal…
We present an information-theoretic approach to lower bound the oracle complexity of nonsmooth black box convex optimization, unifying previous lower bounding techniques by identifying a combinatorial problem, namely string guessing, as a…