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Survey schemes for stochastic gradient descent with applications to M-estimation

arXiv.org Machine Learning

In certain situations that shall be undoubtedly more and more common in the Big Data era, the datasets available are so massive that computing statistics over the full sample is hardly feasible, if not unfeasible. A natural approach in this context consists in using survey schemes and substituting the "full data" statistics with their counterparts based on the resulting random samples, of manageable size. It is the main purpose of this paper to investigate the impact of survey sampling with unequal inclusion probabilities on stochastic gradient descent-based M-estimation methods in large-scale statistical and machine-learning problems. Precisely, we prove that, in presence of some a priori information, one may significantly increase asymptotic accuracy when choosing appropriate first order inclusion probabilities, without affecting complexity. These striking results are described here by limit theorems and are also illustrated by numerical experiments.


An Introduction to Matrix Concentration Inequalities

arXiv.org Machine Learning

In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix concentration inequalities, research has advanced to the point where we can conquer many (formerly) challenging problems with a page or two of arithmetic. The aim of this monograph is to describe the most successful methods from this area along with some interesting examples that these techniques can illuminate.


The SP theory of intelligence: an overview

arXiv.org Artificial Intelligence

This article is an overview of the "SP theory of intelligence". The theory aims to simplify and integrate concepts across artificial intelligence, mainstream computing and human perception and cognition, with information compression as a unifying theme. It is conceived as a brain-like system that receives 'New' information and stores some or all of it in compressed form as 'Old' information. It is realised in the form of a computer model -- a first version of the SP machine. The concept of "multiple alignment" is a powerful central idea. Using heuristic techniques, the system builds multiple alignments that are 'good' in terms of information compression. For each multiple alignment, probabilities may be calculated. These provide the basis for calculating the probabilities of inferences. The system learns new structures from partial matches between patterns. Using heuristic techniques, the system searches for sets of structures that are 'good' in terms of information compression. These are normally ones that people judge to be 'natural', in accordance with the 'DONSVIC' principle -- the discovery of natural structures via information compression. The SP theory may be applied in several areas including 'computing', aspects of mathematics and logic, representation of knowledge, natural language processing, pattern recognition, several kinds of reasoning, information storage and retrieval, planning and problem solving, information compression, neuroscience, and human perception and cognition. Examples include the parsing and production of language including discontinuous dependencies in syntax, pattern recognition at multiple levels of abstraction and its integration with part-whole relations, nonmonotonic reasoning and reasoning with default values, reasoning in Bayesian networks including 'explaining away', causal diagnosis, and the solving of a geometric analogy problem.


Declarative Statistical Modeling with Datalog

arXiv.org Artificial Intelligence

Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the probability space to a conditional subspace (the posterior). Use cases of such formalisms include the development of algorithms in machine learning and artificial intelligence. We propose and investigate a declarative framework for specifying statistical models on top of a database, through an appropriate extension of Datalog. By virtue of extending Datalog, our framework offers a natural integration with the database, and has a robust declarative semantics. Our Datalog extension provides convenient mechanisms to include numerical probability functions; in particular, conclusions of rules may contain values drawn from such functions. The semantics of a program is a probability distribution over the possible outcomes of the input database with respect to the program; these outcomes are minimal solutions with respect to a related program with existentially quantified variables in conclusions. Observations are naturally incorporated by means of integrity constraints over the extensional and intensional relations. We focus on programs that use discrete numerical distributions, but even then the space of possible outcomes may be uncountable (as a solution can be infinite). We define a probability measure over possible outcomes by applying the known concept of cylinder sets to a probabilistic chase procedure. We show that the resulting semantics is robust under different chases. We also identify conditions guaranteeing that all possible outcomes are finite (and then the probability space is discrete). We argue that the framework we propose retains the purely declarative nature of Datalog, and allows for natural specifications of statistical models.


Concave Penalized Estimation of Sparse Gaussian Bayesian Networks

arXiv.org Machine Learning

We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our main contribution is a fast algorithm for score-based structure learning which does not restrict the search space in any way and works on high-dimensional datasets with thousands of variables. Our use of concave regularization, as opposed to the more popular $\ell_0$ (e.g. BIC) penalty, is new. Moreover, we provide theoretical guarantees which generalize existing asymptotic results when the underlying distribution is Gaussian. Most notably, our framework does not require the existence of a so-called faithful DAG representation, and as a result the theory must handle the inherent nonidentifiability of the estimation problem in a novel way. Finally, as a matter of independent interest, we provide a comprehensive comparison of our approach to several standard structure learning methods using open-source packages developed for the R language. Based on these experiments, we show that our algorithm is significantly faster than other competing methods while obtaining higher sensitivity with comparable false discovery rates for high-dimensional data. In particular, the total runtime for our method to generate a solution path of 20 estimates for DAGs with 8000 nodes is around one hour.


Leveraging Multiple Artificial Intelligence Techniques to Improve the Responsiveness in Operations Planning: ASPEN for Orbital Express

AI Magazine

The challenging timeline for DARPA’s Orbital Express mission demanded a flexible, responsive, and (above all) safe approach to mission planning. Mission planning for space is challenging because of the mixture of goals and constraints. Every space mission tries to squeeze all of the capacity possible out of the spacecraft. For Orbital Express, this means performing as many experiments as possible, while still keeping the spacecraft safe. Keeping the spacecraft safe can be very challenging because we need to maintain the correct thermal environment (or batteries might freeze), we need to avoid pointing cameras and sensitive sensors at the sun, we need to keep the spacecraft batteries charged, and we need to keep the two spacecraft from colliding... made more difficult as only one of the spacecraft had thrusters. Because the mission was a technology demonstration, pertinent planning information was learned during actual mission execution. For example, we didn’t know for certain how long it would take to transfer propellant from one spacecraft to the other, although this was a primary mission goal. The only way to find out was to perform the task and monitor how long it actually took. This information led to amendments to procedures, which led to changes in the mission plan. In general, we used the ASPEN planner scheduler to generate and validate the mission plans. ASPEN is a planning system that allows us to enter all of the spacecraft constraints, the resources, the communications windows, and our objectives. ASPEN then could automatically plan our day. We enhanced ASPEN to enable it to reason about uncertainty. We also developed a model generator that would read the text of a procedure and translate it into an ASPEN model. Note that a model is the input to ASPEN that describes constraints, resources, and activities. These technologies had a significant impact on the success of the Orbital Express mission. Finally, we formulated a technique for converting procedural information to declarative information by transforming procedures into models of hierarchical task networks (HTNs). The impact of this effort on the mission was a significant reduction in (1) the execution time of the mission, (2) the daily staff required to produce plans, and (3) planning errors. Not a single miss-configured command was sent during operations.


The Dialog State Tracking Challenge Series

AI Magazine

Dialog state tracking is difficult because automatic speech recognition (ASR) and spoken language understanding (SLU) errors are common and can cause the system to misunderstand the user. At the same time, state tracking is crucial because the system relies on the estimated dialog state to choose actions -- for example, which restaurants to suggest. Figure 1 shows an illustration of the dialog state tracking task. Historically dialog state tracking has been done with handcrafted rules. More recently, statistical methods have been found to be superior by effectively overcoming some SLU errors, resulting in better dialogs. Despite this progress, direct comparisons between methods have not been possible because past studies use different domains, system components, and evaluation measures, hindering progresss.


AAAI Conferences Calendar

AI Magazine

This page includes forthcoming AAAI sponsored conferences, conferences presented by AAAI Affiliates, and conferences held in cooperation with AAAI. AI Magazine also maintains a calendar listing that includes nonaffiliated conferences at www.aaai.org/Magazine/calendar.php. BIOSTEC 2015 will be held January 12-15 in Lisbon, Portugal Twenty-Ninth AAAI Conference on Twenty-Eighth International Florida Artificial Intelligence. AAAI-15 will be AI Research Society Conference. ICPRAM 2015 will be AAAI Spring Symposium.


Space Applications of Artificial Intelligence

AI Magazine

We are pleased to introduce the space application issue articles in this issue of AI Magazine. The exploration of space is a testament to human curiosity and the desire to understand the universe that we inhabit. As many space agencies around the world design and deploy missions, it is apparent that there is a need for intelligent, exploring systems that can make decisions on their own in remote, potentially hostile environments. At the same time, the monetary cost of operating missions, combined with the growing complexity of the instruments and vehicles being deployed, make it apparent that substantial improvements can be made by the judicious use of automation in mission operations.


Automated Scheduling for NASA's Deep Space Network

AI Magazine

This article describes the DSN scheduling wngine (DSE) component of a new scheduling system being deployed for NASA's deep space network. The DSE provides core automation functionality for scheduling the network, including the interpretation of scheduling requirements expressed by users, their elaboration into tracking passes, and the resolution of conflicts and constraint violations. The DSE incorporates both systematic search and repair-based algorithms, used for different phases and purposes in the overall system. It has been integrated with a web application which provides DSE functionality to all DSN users through a standard web browser, as part of a peer-to-peer schedule negotiation process for the entire network. The system has been deployed operationally and is in routine use, and is in the process of being extended to support long-range planning and forecasting, and near-real-time scheduling.