237 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Sum-of-squares representations for copositive matrices and independent sets in graphs

    Get PDF
    A polynomial optimization problem asks for minimizing a polynomial function (cost) given a set of constraints (rules) represented by polynomial inequalities and equations. Many hard problems in combinatorial optimization and applications in operations research can be naturally encoded as polynomial optimization problems. A common approach for addressing such computationally hard problems is by considering variations of the original problem that give an approximate solution, and that can be solved efficiently. One such approach for attacking hard combinatorial problems and, more generally, polynomial optimization problems, is given by the so-called sum-of-squares approximations. This thesis focuses on studying whether these approximations find the optimal solution of the original problem.We investigate this question in two main settings: 1) Copositive programs and 2) parameters dealing with independent sets in graphs. Among our main new results, we characterize the matrix sizes for which sum-of-squares approximations are able to capture all copositive matrices. In addition, we show finite convergence of the sums-of-squares approximations for maximum independent sets in graphs based on their continuous copositive reformulations. We also study sum-of-squares approximations for parameters asking for maximum balanced independent sets in bipartite graphs. In particular, we find connections with the Lovász theta number and we design eigenvalue bounds for several related parameters when the graphs satisfy some symmetry properties.<br/

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    A Strong Composition Theorem for Junta Complexity and the Boosting of Property Testers

    Full text link
    We prove a strong composition theorem for junta complexity and show how such theorems can be used to generically boost the performance of property testers. The ε\varepsilon-approximate junta complexity of a function ff is the smallest integer rr such that ff is ε\varepsilon-close to a function that depends only on rr variables. A strong composition theorem states that if ff has large ε\varepsilon-approximate junta complexity, then g∘fg \circ f has even larger ε′\varepsilon'-approximate junta complexity, even for ε′≫ε\varepsilon' \gg \varepsilon. We develop a fairly complete understanding of this behavior, proving that the junta complexity of g∘fg \circ f is characterized by that of ff along with the multivariate noise sensitivity of gg. For the important case of symmetric functions gg, we relate their multivariate noise sensitivity to the simpler and well-studied case of univariate noise sensitivity. We then show how strong composition theorems yield boosting algorithms for property testers: with a strong composition theorem for any class of functions, a large-distance tester for that class is immediately upgraded into one for small distances. Combining our contributions yields a booster for junta testers, and with it new implications for junta testing. This is the first boosting-type result in property testing, and we hope that the connection to composition theorems adds compelling motivation to the study of both topics.Comment: 44 pages, 1 figure, FOCS 202

    LIPIcs, Volume 274, ESA 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 274, ESA 2023, Complete Volum

    Fundamentals

    Get PDF
    Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    Evaluation of optimal solutions in multicriteria models for intelligent decision support

    Get PDF
    La memoria se enmarca dentro de la optimización y su uso para la toma de decisiones. La secuencia lógica ha sido la modelación, implementación, resolución y validación que conducen a una decisión. Para esto, hemos utilizado herramientas del análisis multicrerio, optimización multiobjetivo y técnicas de inteligencia artificial. El trabajo se ha estructurado en dos partes (divididas en tres capítulos cada una) que se corresponden con la parte teórica y con la parte experimental. En la primera parte se analiza el contexto del campo de estudio con un análisis del marco histórico y posteriormente se dedica un capítulo a la optimización multicriterio en el se recogen modelos conocidos, junto con aportaciones originales de este trabajo. En el tercer capítulo, dedicado a la inteligencia artificial, se presentan los fundamentos del aprendizaje estadístico , las técnicas de aprendizaje automático y de aprendizaje profundo necesarias para las aportaciones en la segunda parte. La segunda parte contiene siete casos reales a los que se han aplicado las técnicas descritas. En el primer capítulo se estudian dos casos: el rendimiento académico de los estudiantes de la Universidad Industrial de Santander (Colombia) y un sistema objetivo para la asignación del premio MVP en la NBA. En el siguiente capítulo se utilizan técnicas de inteligencia artificial a la similitud musical (detección de plagios en Youtube), la predicción del precio de cierre de una empresa en el mercado bursátil de Nueva York y la clasificación automática de señales espaciales acústicas en entornos envolventes. En el último capítulo a la potencia de la inteligencia artificial se le incorporan técnicas de análisis multicriterio para detectar el fracaso escolar universitario de manera precoz (en la Universidad Industrial de Santander) y, para establecer un ranking de modelos de inteligencia artificial de se recurre a métodos multicriterio. Para acabar la memoria, a pesar de que cada capítulo contiene una conclusión parcial, en el capítulo 8 se recogen las principales conclusiones de toda la memoria y una bibliografía bastante exhaustiva de los temas tratados. Además, el trabajo concluye con tres apéndices que contienen los programas y herramientas, que a pesar de ser útiles para la comprensión de la memoria, se ha preferido poner por separado para que los capítulos resulten más fluidos

    High-Dimensional Statistics

    Full text link
    These lecture notes were written for the course 18.657, High Dimensional Statistics at MIT. They build on a set of notes that was prepared at Princeton University in 2013-14 that was modified (and hopefully improved) over the years.Comment: This is the 2017 version of these notes, uploaded to arXiv without any chang
    • …
    corecore