Information-gain computation

Despite large incentives, ecorrectness in software remains an elusive goal. Declarative programming techniques, where algorithms are derived from a specification of the desired behavior, offer hope to address this problem, since there is a combinatorial reduction in complexity in programming in terms of specifications instead of algorithms, and arbitrary desired properties can be expressed and enforced in specifications directly. However, limitations on performance have prevented programming with declarative specifications from becoming a mainstream technique for general-purpose programming. To address the performance bottleneck in deriving an algorithm from a specification, I propose information-gain computation, a framework where an adaptive evaluation strategy is used to efficiently perform a search which derives algorithms that provide information about a query most directly. Within this framework, opportunities to compress the search space present themselves, which suggest that information-theoretic bounds on the performance of such a system might be articulated and a system designed to achieve them. In a preliminary empirical study of adaptive evaluation for a simple test program, the evaluation strategy adapts successfully to evaluate a query efficiently.Comment: Accepted, PLP 2017 (http://www.stoics.org.uk/plp/plp2017/) Revised version of project for Phys 256B @ Davis (http://csc.ucdavis.edu/~chaos/courses/ncaso/) Reduces to practice ideas previously presented in arXiv:1505.00002 and at https://www.meetup.com/SF-Types-Theorems-and-Programming-Languages/events/232908199

Variational Particle Approximations

Approximate inference in high-dimensional, discrete probabilistic models is a central problem in computational statistics and machine learning. This paper describes discrete particle variational inference (DPVI), a new approach that combines key strengths of Monte Carlo, variational and search-based techniques. DPVI is based on a novel family of particle-based variational approximations that can be fit using simple, fast, deterministic search techniques. Like Monte Carlo, DPVI can handle multiple modes, and yields exact results in a well-defined limit. Like unstructured mean-field, DPVI is based on optimizing a lower bound on the partition function; when this quantity is not of intrinsic interest, it facilitates convergence assessment and debugging. Like both Monte Carlo and combinatorial search, DPVI can take advantage of factorization, sequential structure, and custom search operators. This paper defines DPVI particle-based approximation family and partition function lower bounds, along with the sequential DPVI and local DPVI algorithm templates for optimizing them. DPVI is illustrated and evaluated via experiments on lattice Markov Random Fields, nonparametric Bayesian mixtures and block-models, and parametric as well as non-parametric hidden Markov models. Results include applications to real-world spike-sorting and relational modeling problems, and show that DPVI can offer appealing time/accuracy trade-offs as compared to multiple alternatives.Comment: First two authors contributed equally to this wor

GMNN: Graph Markov Neural Networks

This paper studies semi-supervised object classification in relational data, which is a fundamental problem in relational data modeling. The problem has been extensively studied in the literature of both statistical relational learning (e.g. relational Markov networks) and graph neural networks (e.g. graph convolutional networks). Statistical relational learning methods can effectively model the dependency of object labels through conditional random fields for collective classification, whereas graph neural networks learn effective object representations for classification through end-to-end training. In this paper, we propose the Graph Markov Neural Network (GMNN) that combines the advantages of both worlds. A GMNN models the joint distribution of object labels with a conditional random field, which can be effectively trained with the variational EM algorithm. In the E-step, one graph neural network learns effective object representations for approximating the posterior distributions of object labels. In the M-step, another graph neural network is used to model the local label dependency. Experiments on object classification, link classification, and unsupervised node representation learning show that GMNN achieves state-of-the-art results.Comment: icml 201

A Credit Assignment Compiler for Joint Prediction

Many machine learning applications involve jointly predicting multiple mutually dependent output variables. Learning to search is a family of methods where the complex decision problem is cast into a sequence of decisions via a search space. Although these methods have shown promise both in theory and in practice, implementing them has been burdensomely awkward. In this paper, we show the search space can be defined by an arbitrary imperative program, turning learning to search into a credit assignment compiler. Altogether with the algorithmic improvements for the compiler, we radically reduce the complexity of programming and the running time. We demonstrate the feasibility of our approach on multiple joint prediction tasks. In all cases, we obtain accuracies as high as alternative approaches, at drastically reduced execution and programming time

Probabilistic Neural-symbolic Models for Interpretable Visual Question Answering

We propose a new class of probabilistic neural-symbolic models, that have symbolic functional programs as a latent, stochastic variable. Instantiated in the context of visual question answering, our probabilistic formulation offers two key conceptual advantages over prior neural-symbolic models for VQA. Firstly, the programs generated by our model are more understandable while requiring lesser number of teaching examples. Secondly, we show that one can pose counterfactual scenarios to the model, to probe its beliefs on the programs that could lead to a specified answer given an image. Our results on the CLEVR and SHAPES datasets verify our hypotheses, showing that the model gets better program (and answer) prediction accuracy even in the low data regime, and allows one to probe the coherence and consistency of reasoning performed.Comment: ICML 2019 Camera Ready + Appendi

Hinge-Loss Markov Random Fields and Probabilistic Soft Logic

A fundamental challenge in developing high-impact machine learning technologies is balancing the need to model rich, structured domains with the ability to scale to big data. Many important problem areas are both richly structured and large scale, from social and biological networks, to knowledge graphs and the Web, to images, video, and natural language. In this paper, we introduce two new formalisms for modeling structured data, and show that they can both capture rich structure and scale to big data. The first, hinge-loss Markov random fields (HL-MRFs), is a new kind of probabilistic graphical model that generalizes different approaches to convex inference. We unite three approaches from the randomized algorithms, probabilistic graphical models, and fuzzy logic communities, showing that all three lead to the same inference objective. We then define HL-MRFs by generalizing this unified objective. The second new formalism, probabilistic soft logic (PSL), is a probabilistic programming language that makes HL-MRFs easy to define using a syntax based on first-order logic. We introduce an algorithm for inferring most-probable variable assignments (MAP inference) that is much more scalable than general-purpose convex optimization methods, because it uses message passing to take advantage of sparse dependency structures. We then show how to learn the parameters of HL-MRFs. The learned HL-MRFs are as accurate as analogous discrete models, but much more scalable. Together, these algorithms enable HL-MRFs and PSL to model rich, structured data at scales not previously possible

Adaptive Neighborhood Graph Construction for Inference in Multi-Relational Networks

A neighborhood graph, which represents the instances as vertices and their relations as weighted edges, is the basis of many semi-supervised and relational models for node labeling and link prediction. Most methods employ a sequential process to construct the neighborhood graph. This process often consists of generating a candidate graph, pruning the candidate graph to make a neighborhood graph, and then performing inference on the variables (i.e., nodes) in the neighborhood graph. In this paper, we propose a framework that can dynamically adapt the neighborhood graph based on the states of variables from intermediate inference results, as well as structural properties of the relations connecting them. A key strength of our framework is its ability to handle multi-relational data and employ varying amounts of relations for each instance based on the intermediate inference results. We formulate the link prediction task as inference on neighborhood graphs, and include preliminary results illustrating the effects of different strategies in our proposed framework.Comment: Presented at SIGKDD 12th International Workshop on Mining and Learning with Graphs (MLG'16

Cognitive Database: A Step towards Endowing Relational Databases with Artificial Intelligence Capabilities

We propose Cognitive Databases, an approach for transparently enabling Artificial Intelligence (AI) capabilities in relational databases. A novel aspect of our design is to first view the structured data source as meaningful unstructured text, and then use the text to build an unsupervised neural network model using a Natural Language Processing (NLP) technique called word embedding. This model captures the hidden inter-/intra-column relationships between database tokens of different types. For each database token, the model includes a vector that encodes contextual semantic relationships. We seamlessly integrate the word embedding model into existing SQL query infrastructure and use it to enable a new class of SQL-based analytics queries called cognitive intelligence (CI) queries. CI queries use the model vectors to enable complex queries such as semantic matching, inductive reasoning queries such as analogies, predictive queries using entities not present in a database, and, more generally, using knowledge from external sources. We demonstrate unique capabilities of Cognitive Databases using an Apache Spark based prototype to execute inductive reasoning CI queries over a multi-modal database containing text and images. We believe our first-of-a-kind system exemplifies using AI functionality to endow relational databases with capabilities that were previously very hard to realize in practice

Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs

We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If carried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider three kinds of approximations: canonical orderings of sequences, functions with $k$-order interactions, and stochastic optimization algorithms with random permutations. Our framework unifies a variety of existing work in the literature, and suggests possible modeling and algorithmic extensions. We explore a few in our experiments, which demonstrate improved performance over current state-of-the-art methods.Comment: This version clarifies and adds detail to some of the argument

Ensemble Relational Learning based on Selective Propositionalization

Dealing with structured data needs the use of expressive representation formalisms that, however, puts the problem to deal with the computational complexity of the machine learning process. Furthermore, real world domains require tools able to manage their typical uncertainty. Many statistical relational learning approaches try to deal with these problems by combining the construction of relevant relational features with a probabilistic tool. When the combination is static (static propositionalization), the constructed features are considered as boolean features and used offline as input to a statistical learner; while, when the combination is dynamic (dynamic propositionalization), the feature construction and probabilistic tool are combined into a single process. In this paper we propose a selective propositionalization method that search the optimal set of relational features to be used by a probabilistic learner in order to minimize a loss function. The new propositionalization approach has been combined with the random subspace ensemble method. Experiments on real-world datasets shows the validity of the proposed method.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1006.518