6 research outputs found
Probabilistic abductive logic programming using Dirichlet priors
Probabilistic programming is an area of research that aims to develop general inference algorithms for probabilistic models expressed as probabilistic programs whose execution corresponds to inferring the parameters of those models. In this paper, we introduce a probabilistic programming language (PPL) based on abductive logic programming for performing inference in probabilistic models involving categorical distributions with Dirichlet priors. We encode these models as abductive logic programs enriched with probabilistic definitions and queries, and show how to execute and compile them to boolean formulas. Using the latter, we perform generalized inference using one of two proposed Markov Chain Monte Carlo (MCMC) sampling algorithms: an adaptation of uncollapsed Gibbs sampling from related work and a novel collapsed Gibbs sampling (CGS). We show that CGS converges faster than the uncollapsed version on a latent Dirichlet allocation (LDA) task using synthetic data. On similar data, we compare our PPL with LDA-specific algorithms and other PPLs. We find that all methods, except one, perform similarly and that the more expressive the PPL, the slower it is. We illustrate applications of our PPL on real data in two variants of LDA models (Seed and Cluster LDA), and in the repeated insertion model (RIM). In the latter, our PPL yields similar conclusions to inference with EM for Mallows models
Recommended from our members
Ranking facts for explaining answers to elementary science questions
In multiple-choice exams, students select one answer from among typically four choices and can explain why they made that particular choice. Students are good at understanding natural language questions and based on their domain knowledge can easily infer the question's answer by “connecting the dots” across various pertinent facts. Considering automated reasoning for elementary science question answering, we address the novel task of generating explanations for answers from human-authored facts. For this, we examine the practically scalable framework of feature-rich support vector machines leveraging domain-targeted, hand-crafted features. Explanations are created from a human-annotated set of nearly 5000 candidate facts in the WorldTree corpus. Our aim is to obtain better matches for valid facts of an explanation for the correct answer of a question over the available fact candidates. To this end, our features offer a comprehensive linguistic and semantic unification paradigm. The machine learning problem is the preference ordering of facts, for which we test pointwise regression versus pairwise learning-to-rank. Our contributions, originating from comprehensive evaluations against nine existing systems, are (1) a case study in which two preference ordering approaches are systematically compared, and where the pointwise approach is shown to outperform the pairwise approach, thus adding to the existing survey of observations on this topic; (2) since our system outperforms a highly-effective TF-IDF-based IR technique by 3.5 and 4.9 points on the development and test sets, respectively, it demonstrates some of the further task improvement possibilities (e.g., in terms of an efficient learning algorithm, semantic features) on this task; (3) it is a practically competent approach that can outperform some variants of BERT-based reranking models; and (4) the human-engineered features make it an interpretable machine learning model for the task
Collective decision-making under the influence of bribers and temporal constraints
Jo estudio la connexió entre la corrupció i les característiques estructurals dels parlaments: nombre de seients, el nombre de partits representats, i regles de decisió adoptades. Amb l'aplicació d'enfocaments analítics i computacionals, a més de simulacions, mostro que el nombre mitjà de diputats que han de ser subornats disminueix a mesura que el nombre de partits augmenta, de manera que el suborn se sent encoratjat per un nombre cada vegada més gran de parts.
També investigo dues formes en que pot afectar el temps a la presa de decisions. En primer lloc, suggereixo un procediment de votació iteratiu en el que el retard en prendre una decisió és costós. Amb dos electors, dues opcions i un ordre de votació fix, demostro que en l’únic equilibri perfecte en subjocs, l’elector que vota primer, obté la seva opció preferida a l'inici del procediment. Si l'ordre s'inverteix en algun moment, identifico la condició sota la qual el votant que vota segon pot obtenir la seva opció preferida al principi.
En segon lloc, proposo un altre procediment de votació iterativa, permetent que els votants canvien els seus vots, però ara amb una data límit: una etapa que, si no s'ha pres una decisió, els resultats de la votació són pitjors. Mostro que (i) si hi ha temps suficient perquè tots els votants canviïn el seu vot, es prendrà una decisió, i (ii) si hi ha una alternativa preferida per la majoria dels votants, aquesta alternativa serà finalment triada. Afegeixo un estudi experimental que indica que fins i tot amb menys temps del necessari per a què cada votant pugui canviar el seu vot, els electors estaran d'acord amb una decisió de totes maneres.Estudio la conexión entre la corrupción y las características estructurales de los parlamentos: número de asientos, el número de partidos representados, y reglas de decisión adoptadas. Con la aplicación de enfoques analíticos y computacionales, además de simulaciones, muestro que el número medio de diputados que deben ser sobornados disminuye a medida que el número de partidos aumenta, por lo que el soborno se siente alentado por un número cada vez mayor de partes.
También investigo dos formas en que puede afectar el tiempo en la toma de decisiones. En primer lugar, sugiero un procedimiento de votación iterativo en el que el retraso en tomar una decisión es costoso. Con dos electores, dos opciones y un orden de votación fijo, demuestro que en el único equilibrio perfecto en subjuegos, el elector que vota primero obtiene su opción preferida al inicio del procedimiento. Si el orden se invierte en algún momento, identifico la condición bajo la cual el votante que vota segundo puede obtener su opción preferida al principio.
En segundo lugar, propongo otro procedimiento de votación iterativa, permitiendo que los votantes cambian sus votos, pero ahora con una fecha límite: una etapa que, si no se ha tomado una decisión, los resultados de la votación son peores. Muestro que (i) si hay tiempo suficiente para que todos los votantes cambien su voto, se tomará una decisión, y (ii) si hay una alternativa preferida por la mayoría de los votantes, esta alternativa será finalmente elegida. Añado un estudio experimental que indica que los electores estarán de acuerdo con una decisión aunque no haya tiempo sufficiente para que cada votante pueda cambiar su voto.I study the connection between corruption and structural characteristics of parliaments: number of seats, the number of parties represented, and decision rules adopted. Applying analytical and computational approaches, and running simulations, I show that the average number of deputies needed to be bribed decreases as the number of parties increases, so bribery is encouraged by a growing number of parties.
I also investigate two ways in which time may affect decision-making. First, I suggest an iterative voting procedure in which delay to reach a decision is costly. For two voters and two options, with a fixed voting order, I prove that in the unique subgame perfect equilibrium the voter who votes first obtains his most preferred option at the beginning of the procedure. If the fixed order is reversed once at some stage, I identify the condition under which the voter initially voting the second obtains this most preferred option, also at the beginning.
Second, I propose another iterative voting procedure, allowing voters to change their votes, but now with a deadline: a stage such that, if no decision has been taken by then, the worst outcome results. I show that (i) if there is enough time for all the voters to change their vote, a decision will be taken, and (ii) if there is an alternative preferred by a majority of the voters, this alternative will be finally chosen. I add an experimental study indicating that even with less time necessary for every voter to change his vote, the voters will agree with a decision anyway
Recommended from our members
Fundamental Tradeoffs for Modeling Customer Preferences in Revenue Management
Revenue management (RM) is the science of selling the right product, to the right person, at the right price. A key to the success of RM, which now spans a broad array of industries, is its grounding in mathematical modeling and analytics. This dissertation contributes to the development of new RM tools by: (1) exploring some fundamental tradeoffs underlying any RM problems, and (2) designing efficient algorithms for some RM applications. Another underlying theme of this dissertation is the modeling of customer preferences, a key component of any RM problem.
The first chapters of this dissertation focus on the model selection problem: many demand models are available but picking the right model is a challenging task. In particular, we explore the tension between the richness of a model and its tractability. To quantify this tradeoff, we focus on the assortment optimization problem, a very general and core RM problem. To capture customer preferences in this context, we use choice models, a particular type of demand model. In Chapters 1, 2, 3 and 4 we design efficient algorithms for the assortment optimization problem under different choice models. By assessing the strengths and weaknesses of different choice models, we can quantify the cost in tractability one has to pay for better predictive power. This in turn leads to a better understanding of the tradeoffs underlying the model selection problem.
In Chapter 5, we focus on a different question underlying any RM problem: choos- ing how to sell a given product. We illustrate this tradeoff by focusing on the problem of selling ad impressions via Internet display advertising platforms. In particular, we study how the presence of risk-averse buyers affects the desire for reservation con- tracts over real time buy via a second-price auction. In order to capture the risk aversion of buyers, we study different utility models