arXiv subjects

Alexander Gray

Publications and source records attributed to Alexander Gray.

At least 37 records · Page 2Linked to original sources

arXiv2021

Logical Credal Networks

This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional probability bounds of logic formulas, this logic specifies a set of probability distributions over all interpretations. On the one hand, our approach allows propositional and first-order logic formulas with few restrictions, e.g., without requiring acyclicity. On the other hand, it has a Markov condition similar to Bayesian networks and Markov random fields that is critical in real-world applications. Having both these properties makes this logic unique, and we investigate its performance on maximum a posteriori inference tasks, including solving Mastermind games with uncertainty and detecting credit card fraud. The results show that the proposed method outperforms existing approaches, and its advantage lies in aggregating multiple sources of imprecise information.

cs.AI↗

arXiv2021

Combining Rules and Embeddings via Neuro-Symbolic AI for Knowledge Base Completion

Recent interest in Knowledge Base Completion (KBC) has led to a plethora of approaches based on reinforcement learning, inductive logic programming and graph embeddings. In particular, rule-based KBC has led to interpretable rules while being comparable in performance with graph embeddings. Even within rule-based KBC, there exist different approaches that lead to rules of varying quality and previous work has not always been precise in highlighting these differences. Another issue that plagues most rule-based KBC is the non-uniformity of relation paths: some relation sequences occur in very few paths while others appear very frequently. In this paper, we show that not all rule-based KBC models are the same and propose two distinct approaches that learn in one case: 1) a mixture of relations and the other 2) a mixture of paths. When implemented on top of neuro-symbolic AI, which learns rules by extending Boolean logic to real-valued logic, the latter model leads to superior KBC accuracy outperforming state-of-the-art rule-based KBC by 2-10% in terms of mean reciprocal rank. Furthermore, to address the non-uniformity of relation paths, we combine rule-based KBC with graph embeddings thus improving our results even further and achieving the best of both worlds.

cs.AI↗

arXiv2021

LNN-EL: A Neuro-Symbolic Approach to Short-text Entity Linking

Entity linking (EL), the task of disambiguating mentions in text by linking them to entities in a knowledge graph, is crucial for text understanding, question answering or conversational systems. Entity linking on short text (e.g., single sentence or question) poses particular challenges due to limited context. While prior approaches use either heuristics or black-box neural methods, here we propose LNN-EL, a neuro-symbolic approach that combines the advantages of using interpretable rules based on first-order logic with the performance of neural learning. Even though constrained to using rules, LNN-EL performs competitively against SotA black-box neural approaches, with the added benefits of extensibility and transferability. In particular, we show that we can easily blend existing rule templates given by a human expert, with multiple types of features (priors, BERT encodings, box embeddings, etc), and even scores resulting from previous EL methods, thus improving on such methods. For instance, on the LC-QuAD-1.0 dataset, we show more than $4$\% increase in F1 score over previous SotA. Finally, we show that the inductive bias offered by using logic results in learned rules that transfer well across datasets, even without fine tuning, while maintaining high accuracy.

cs.CL↗

arXiv2021

Leveraging Abstract Meaning Representation for Knowledge Base Question Answering

Knowledge base question answering (KBQA)is an important task in Natural Language Processing. Existing approaches face significant challenges including complex question understanding, necessity for reasoning, and lack of large end-to-end training datasets. In this work, we propose Neuro-Symbolic Question Answering (NSQA), a modular KBQA system, that leverages (1) Abstract Meaning Representation (AMR) parses for task-independent question understanding; (2) a simple yet effective graph transformation approach to convert AMR parses into candidate logical queries that are aligned to the KB; (3) a pipeline-based approach which integrates multiple, reusable modules that are trained specifically for their individual tasks (semantic parser, entity andrelationship linkers, and neuro-symbolic reasoner) and do not require end-to-end training data. NSQA achieves state-of-the-art performance on two prominent KBQA datasets based on DBpedia (QALD-9 and LC-QuAD1.0). Furthermore, our analysis emphasizes that AMR is a powerful tool for KBQA systems.

cs.CL↗

arXiv2021

Reinforcement Learning with External Knowledge by using Logical Neural Networks

Conventional deep reinforcement learning methods are sample-inefficient and usually require a large number of training trials before convergence. Since such methods operate on an unconstrained action set, they can lead to useless actions. A recent neuro-symbolic framework called the Logical Neural Networks (LNNs) can simultaneously provide key-properties of both neural networks and symbolic logic. The LNNs functions as an end-to-end differentiable network that minimizes a novel contradiction loss to learn interpretable rules. In this paper, we utilize LNNs to define an inference graph using basic logical operations, such as AND and NOT, for faster convergence in reinforcement learning. Specifically, we propose an integrated method that enables model-free reinforcement learning from external knowledge sources in an LNNs-based logical constrained framework such as action shielding and guide. Our results empirically demonstrate that our method converges faster compared to a model-free reinforcement learning method that doesn't have such logical constraints.

cs.AI↗

arXiv2021

Logic Embeddings for Complex Query Answering

Answering logical queries over incomplete knowledge bases is challenging because: 1) it calls for implicit link prediction, and 2) brute force answering of existential first-order logic queries is exponential in the number of existential variables. Recent work of query embeddings provides fast querying, but most approaches model set logic with closed regions, so lack negation. Query embeddings that do support negation use densities that suffer drawbacks: 1) only improvise logic, 2) use expensive distributions, and 3) poorly model answer uncertainty. In this paper, we propose Logic Embeddings, a new approach to embedding complex queries that uses Skolemisation to eliminate existential variables for efficient querying. It supports negation, but improves on density approaches: 1) integrates well-studied t-norm logic and directly evaluates satisfiability, 2) simplifies modeling with truth values, and 3) models uncertainty with truth bounds. Logic Embeddings are competitively fast and accurate in query answering over large, incomplete knowledge graphs, outperform on negation queries, and in particular, provide improved modeling of answer uncertainty as evidenced by a superior correlation between answer set size and embedding entropy.

cs.AI↗

arXiv2020

Leveraging Semantic Parsing for Relation Linking over Knowledge Bases

Knowledgebase question answering systems are heavily dependent on relation extraction and linking modules. However, the task of extracting and linking relations from text to knowledgebases faces two primary challenges; the ambiguity of natural language and lack of training data. To overcome these challenges, we present SLING, a relation linking framework which leverages semantic parsing using Abstract Meaning Representation (AMR) and distant supervision. SLING integrates multiple relation linking approaches that capture complementary signals such as linguistic cues, rich semantic representation, and information from the knowledgebase. The experiments on relation linking using three KBQA datasets; QALD-7, QALD-9, and LC-QuAD 1.0 demonstrate that the proposed approach achieves state-of-the-art performance on all benchmarks.

cs.CL↗

arXiv2020

Logical Neural Networks

We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning, including classical first-order logic theorem proving as a special case. The model is end-to-end differentiable, and learning minimizes a novel loss function capturing logical contradiction, yielding resilience to inconsistent knowledge. It also enables the open-world assumption by maintaining bounds on truth values which can have probabilistic semantics, yielding resilience to incomplete knowledge.

cs.AI↗

arXiv2020

AutoAIViz: Opening the Blackbox of Automated Artificial Intelligence with Conditional Parallel Coordinates

Artificial Intelligence (AI) can now automate the algorithm selection, feature engineering, and hyperparameter tuning steps in a machine learning workflow. Commonly known as AutoML or AutoAI, these technologies aim to relieve data scientists from the tedious manual work. However, today's AutoAI systems often present only limited to no information about the process of how they select and generate model results. Thus, users often do not understand the process, neither do they trust the outputs. In this short paper, we provide a first user evaluation by 10 data scientists of an experimental system, AutoAIViz, that aims to visualize AutoAI's model generation process. We find that the proposed system helps users to complete the data science tasks, and increases their understanding, toward the goal of increasing trust in the AutoAI system.

cs.LG↗

arXiv2019

An ADMM Based Framework for AutoML Pipeline Configuration

We study the AutoML problem of automatically configuring machine learning pipelines by jointly selecting algorithms and their appropriate hyper-parameters for all steps in supervised learning pipelines. This black-box (gradient-free) optimization with mixed integer & continuous variables is a challenging problem. We propose a novel AutoML scheme by leveraging the alternating direction method of multipliers (ADMM). The proposed framework is able to (i) decompose the optimization problem into easier sub-problems that have a reduced number of variables and circumvent the challenge of mixed variable categories, and (ii) incorporate black-box constraints along-side the black-box optimization objective. We empirically evaluate the flexibility (in utilizing existing AutoML techniques), effectiveness (against open source AutoML toolkits),and unique capability (of executing AutoML with practically motivated black-box constraints) of our proposed scheme on a collection of binary classification data sets from UCI ML& OpenML repositories. We observe that on an average our framework provides significant gains in comparison to other AutoML frameworks (Auto-sklearn & TPOT), highlighting the practical advantages of this framework.

cs.LG↗

arXiv2019

How can AI Automate End-to-End Data Science?

Data science is labor-intensive and human experts are scarce but heavily involved in every aspect of it. This makes data science time consuming and restricted to experts with the resulting quality heavily dependent on their experience and skills. To make data science more accessible and scalable, we need its democratization. Automated Data Science (AutoDS) is aimed towards that goal and is emerging as an important research and business topic. We introduce and define the AutoDS challenge, followed by a proposal of a general AutoDS framework that covers existing approaches but also provides guidance for the development of new methods. We categorize and review the existing literature from multiple aspects of the problem setup and employed techniques. Then we provide several views on how AI could succeed in automating end-to-end AutoDS. We hope this survey can serve as insightful guideline for the AutoDS field and provide inspiration for future research.

cs.AI↗

arXiv2019

Human-AI Collaboration in Data Science: Exploring Data Scientists' Perceptions of Automated AI

The rapid advancement of artificial intelligence (AI) is changing our lives in many ways. One application domain is data science. New techniques in automating the creation of AI, known as AutoAI or AutoML, aim to automate the work practices of data scientists. AutoAI systems are capable of autonomously ingesting and pre-processing data, engineering new features, and creating and scoring models based on a target objectives (e.g. accuracy or run-time efficiency). Though not yet widely adopted, we are interested in understanding how AutoAI will impact the practice of data science. We conducted interviews with 20 data scientists who work at a large, multinational technology company and practice data science in various business settings. Our goal is to understand their current work practices and how these practices might change with AutoAI. Reactions were mixed: while informants expressed concerns about the trend of automating their jobs, they also strongly felt it was inevitable. Despite these concerns, they remained optimistic about their future job security due to a view that the future of data science work will be a collaboration between humans and AI systems, in which both automation and human expertise are indispensable.

cs.HC↗

arXiv2013

Local Support Vector Machines:Formulation and Analysis

We provide a formulation for Local Support Vector Machines (LSVMs) that generalizes previous formulations, and brings out the explicit connections to local polynomial learning used in nonparametric estimation literature. We investigate the simplest type of LSVMs called Local Linear Support Vector Machines (LLSVMs). For the first time we establish conditions under which LLSVMs make Bayes consistent predictions at each test point $x_0$. We also establish rates at which the local risk of LLSVMs converges to the minimum value of expected local risk at each point $x_0$. Using stability arguments we establish generalization error bounds for LLSVMs.

stat.ML↗

arXiv2013

Stochastic ADMM for Nonsmooth Optimization

We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers (ADMM) algorithm. Our algorithm applies to a more general class of nonsmooth convex functions that does not necessarily have a closed-form solution by minimizing the augmented function directly. We also demonstrate the rates of convergence for our algorithm under various structural assumptions of the stochastic functions: $O(1/\sqrt{t})$ for convex functions and $O(\log t/t)$ for strongly convex functions. Compared to previous literature, we establish the convergence rate of ADMM algorithm, for the first time, in terms of both the objective value and the feasibility violation.

cs.LG↗

arXiv2012

Stochastic Smoothing for Nonsmooth Minimizations: Accelerating SGD by Exploiting Structure

In this work we consider the stochastic minimization of nonsmooth convex loss functions, a central problem in machine learning. We propose a novel algorithm called Accelerated Nonsmooth Stochastic Gradient Descent (ANSGD), which exploits the structure of common nonsmooth loss functions to achieve optimal convergence rates for a class of problems including SVMs. It is the first stochastic algorithm that can achieve the optimal O(1/t) rate for minimizing nonsmooth loss functions (with strong convexity). The fast rates are confirmed by empirical comparisons, in which ANSGD significantly outperforms previous subgradient descent algorithms including SGD.

cs.LG↗

arXiv2011

UPAL: Unbiased Pool Based Active Learning

In this paper we address the problem of pool based active learning, and provide an algorithm, called UPAL, that works by minimizing the unbiased estimator of the risk of a hypothesis in a given hypothesis space. For the space of linear classifiers and the squared loss we show that UPAL is equivalent to an exponentially weighted average forecaster. Exploiting some recent results regarding the spectra of random matrices allows us to establish consistency of UPAL when the true hypothesis is a linear hypothesis. Empirical comparison with an active learner implementation in Vowpal Wabbit, and a previously proposed pool based active learner implementation show good empirical performance and better scalability.

stat.ML↗

arXiv2011

Data-Distributed Weighted Majority and Online Mirror Descent

In this paper, we focus on the question of the extent to which online learning can benefit from distributed computing. We focus on the setting in which $N$ agents online-learn cooperatively, where each agent only has access to its own data. We propose a generic data-distributed online learning meta-algorithm. We then introduce the Distributed Weighted Majority and Distributed Online Mirror Descent algorithms, as special cases. We show, using both theoretical analysis and experiments, that compared to a single agent: given the same computation time, these distributed algorithms achieve smaller generalization errors; and given the same generalization errors, they can be $N$ times faster.

cs.LG↗

arXiv2007

The Three-Point Correlation Function of Luminous Red Galaxies in the Sloan Digital Sky Survey

We present measurements of the redshift-space three-point correlation function of 50,967 Luminous Red Galaxies (LRGs) from Data Release 3 (DR3) of the Sloan Digital Sky Survey (SDSS). We have studied the shape dependence of the reduced three-point correlation function (Qz(s,q,theta)) on three different scales, s=4, 7 and 10 h-1 Mpc, and over the range of 1 < q < 3 and 0 < theta < 180. On small scales (s=4 h-1 Mpc), Qz is nearly constant, with little change as a function of q and theta. However, there is evidence for a shallow U-shaped behaviour (with theta) which is expected from theoretical modeling of Qz . On larger scales (s=7 and 10 h-1 Mpc), the U-shaped anisotropy in Qz (with theta) is more clearly detected. We compare this shape-dependence in Qz(s,q,theta) with that seen in mock galaxy catalogues which were generated by populating the dark matter halos in large N-body simulations with mock galaxies using various Halo Occupation Distributions (HOD). We find that the combination of the observed number density of LRGs, the (redshift-space) two-point correlation function and Qz provides a strong constraint on the allowed HOD parameters (M_min, M_1, alpha) and breaks key degeneracies between these parameters. For example, our observed Qz disfavors mock catalogues that overpopulate massive dark matter halos with many LRG satellites. We also estimate the linear bias of LRGs to be b=1.87+/-0.07 in excellent agreement with other measurements.

astro-ph↗