Related papers: AdaBoost Does Not Always Cycle: A Computer-Assiste…
This manuscript provides optimization guarantees, generalization bounds, and statistical consistency results for AdaBoost variants which replace the exponential loss with the logistic and similar losses (specifically, twice differentiable…
We study dynamical decoupling in a multi-qubit setting, where it is combined with quantum logic gates. This is illustrated in terms of computation using Heisenberg interactions only, where global decoupling pulses commute with the…
We construct a countable family of multi-dimensional continued fraction algorithms, built out of five specific multidimensional continued fractions, and find a wide class of cubic irrational real numbers a so that either (a, a^2) or (a,…
We obtain a complete characterization of all orbits of a quadratic Collatz-type recursion called the divide-or-choose-2 rule. Each orbit either ends in a cycle whose period depends on the initial value or it goes to infinity. We specify…
Boosting is an ensemble learning method that converts a weak learner into a strong learner in the PAC learning framework. Freund and Schapire designed the Godel prize-winning algorithm named AdaBoost that can boost learners, which output…
We study boosting algorithms from a new perspective. We show that the Lagrange dual problems of AdaBoost, LogitBoost and soft-margin LPBoost with generalized hinge loss are all entropy maximization problems. By looking at the dual problems…
We consider an independently identically distributed random dynamical system generated by finitely many, non-uniformly expanding Markov interval maps with a finite number of branches. Assuming a topologically mixing condition and the…
Based on the use of different exponential bases to define class-dependent error bounds, a new and highly efficient asymmetric boosting scheme, coined as AdaBoostDB (Double-Base), is proposed. Supported by a fully theoretical derivation…
Consideration of the primal and dual problems together leads to important new insights into the characteristics of boosting algorithms. In this work, we propose a general framework that can be used to design new boosting algorithms. A wide…
We introduce a useful tool for analyzing boosting algorithms called the ``smooth margin function,'' a differentiable approximation of the usual margin for boosting algorithms. We present two boosting algorithms based on this smooth margin,…
In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
We investigate the Brusselator system with diffusion and Dirichlet boundary conditions on one dimensional space interval. Our proof demonstrates that, for certain parameter values, a periodic orbit exists. This proof is computer-assisted…
The significance of the study of the theoretical and practical properties of AdaBoost is unquestionable, given its simplicity, wide practical use, and effectiveness on real-world datasets. Here we present a few open problems regarding the…
Gradient descent is arguably one of the most popular online optimization methods with a wide array of applications. However, the standard implementation where agents simultaneously update their strategies yields several undesirable…
Asynchronous-parallel algorithms have the potential to vastly speed up algorithms by eliminating costly synchronization. However, our understanding to these algorithms is limited because the current convergence of asynchronous (block)…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
Boosting methods have been introduced in the late 1980's. They were born following the theoritical aspect of PAC learning. The main idea of boosting methods is to combine weak learners to obtain a strong learner. The weak learners are…
We study a quantum Otto cycle that uses a 2-qubit working substance whose Hamiltonian does not commute with itself at different times during unitary strokes. We investigate how the cycle responds to the loss of quantum adiabaticity when…
We study a class of multi-period online decision-making problems with sequence-based predictions, which may be generated by machine learning models but whose accuracy is not guaranteed. In each period, the decision-maker observes the…