Alexander Gray

Keerthiram Murugesan, Sarathkrishna Swaminathan, Soham Dan et al.

With the growing interest in large language models, the need for evaluating the quality of machine text compared to reference (typically human-generated) text has become focal attention. Most recent works focus either on task-specific evaluation metrics or study the properties of machine-generated text captured by the existing metrics. In this work, we propose a new evaluation scheme to model human judgments in 7 NLP tasks, based on the fine-grained mismatches between a pair of texts. Inspired by the recent efforts in several NLP tasks for fine-grained evaluation, we introduce a set of 13 mismatch error types such as spatial/geographic errors, entity errors, etc, to guide the model for better prediction of human judgments. We propose a neural framework for evaluating machine texts that uses these mismatch error types as auxiliary tasks and re-purposes the existing single-number evaluation metrics as additional scalar features, in addition to textual features extracted from the machine and reference texts. Our experiments reveal key insights about the existing metrics via the mismatch errors. We show that the mismatch errors between the sentence pairs on the held-out datasets from 7 NLP tasks align well with the human evaluation.

Parikshit Ram, Alexander G. Gray, Horst C. Samulowitz et al.

We show, to our knowledge, the first theoretical treatments of two common questions in cross-validation based hyperparameter selection: (1) After selecting the best hyperparameter using a held-out set, we train the final model using {\em all} of the training data -- since this may or may not improve future generalization error, should one do this? (2) During optimization such as via SGD (stochastic gradient descent), we must set the optimization tolerance $ρ$ -- since it trades off predictive accuracy with computation cost, how should one set it? Toward these problems, we introduce the {\em hold-in risk} (the error due to not using the whole training data), and the {\em model class mis-specification risk} (the error due to having chosen the wrong model class) in a theoretical view which is simple, general, and suggests heuristics that can be used when faced with a dataset instance. In proof-of-concept studies in synthetic data where theoretical quantities can be controlled, we show that these heuristics can, respectively, (1) always perform at least as well as always performing retraining or never performing retraining, (2) either improve performance or reduce computational overhead by $2\times$ with no loss in predictive performance.

Tim Klinger, Luke Liu, Soham Dan et al.

Compositional generalization is a key ability of humans that enables us to learn new concepts from only a handful examples. Neural machine learning models, including the now ubiquitous Transformers, struggle to generalize in this way, and typically require thousands of examples of a concept during training in order to generalize meaningfully. This difference in ability between humans and artificial neural architectures, motivates this study on a neuro-symbolic architecture called the Compositional Program Generator (CPG). CPG has three key features: \textit{modularity}, \textit{composition}, and \textit{abstraction}, in the form of grammar rules, that enable it to generalize both systematically to new concepts in a few-shot manner, as well as productively by length on various sequence-to-sequence language tasks. For each input, CPG uses a grammar of the input language and a parser to generate a parse in which each grammar rule is assigned its own unique semantic module, a probabilistic copy or substitution program. Instances with the same parse are always processed with the same composed modules, while those with different parses may be processed with different modules. CPG learns parameters for the modules and is able to learn the semantics for new rules and types incrementally, without forgetting or retraining on rules it's already seen. It achieves perfect generalization on both the SCAN and COGS benchmarks using just 14 examples for SCAN and 22 examples for COGS -- state-of-the-art accuracy with a 1000x improvement in sample efficiency.

Bowen Li, Zhaoyu Li, Qiwei Du et al.

Recent years have witnessed the rapid development of Neuro-Symbolic (NeSy) AI systems, which integrate symbolic reasoning into deep neural networks. However, most of the existing benchmarks for NeSy AI fail to provide long-horizon reasoning tasks with complex multi-agent interactions. Furthermore, they are usually constrained by fixed and simplistic logical rules over limited entities, making them far from real-world complexities. To address these crucial gaps, we introduce LogiCity, the first simulator based on customizable first-order logic (FOL) for an urban-like environment with multiple dynamic agents. LogiCity models diverse urban elements using semantic and spatial concepts, such as IsAmbulance(X) and IsClose(X, Y). These concepts are used to define FOL rules that govern the behavior of various agents. Since the concepts and rules are abstractions, they can be universally applied to cities with any agent compositions, facilitating the instantiation of diverse scenarios. Besides, a key feature of LogiCity is its support for user-configurable abstractions, enabling customizable simulation complexities for logical reasoning. To explore various aspects of NeSy AI, LogiCity introduces two tasks, one features long-horizon sequential decision-making, and the other focuses on one-step visual reasoning, varying in difficulty and agent behaviors. Our extensive evaluation reveals the advantage of NeSy frameworks in abstract reasoning. Moreover, we highlight the significant challenges of handling more complex abstractions in long-horizon multi-agent scenarios or under high-dimensional, imbalanced data. With its flexible design, various features, and newly raised challenges, we believe LogiCity represents a pivotal step forward in advancing the next generation of NeSy AI. All the code and data are open-sourced at our website: https://jaraxxus-me.github.io/LogiCity/

Daiki Kimura, Subhajit Chaudhury, Masaki Ono et al.

We present Logical Optimal Actions (LOA), an action decision architecture of reinforcement learning applications with a neuro-symbolic framework which is a combination of neural network and symbolic knowledge acquisition approach for natural language interaction games. The demonstration for LOA experiments consists of a web-based interactive platform for text-based games and visualization for acquired knowledge for improving interpretability for trained rules. This demonstration also provides a comparison module with other neuro-symbolic approaches as well as non-symbolic state-of-the-art agent models on the same text-based games. Our LOA also provides open-sourced implementation in Python for the reinforcement learning environment to facilitate an experiment for studying neuro-symbolic agents. Code: https://github.com/ibm/loa

Sijia Liu, Parikshit Ram, Deepak Vijaykeerthy et al.

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.

Parikshit Ram, Tim Klinger, Alexander G. Gray

Compositionality is thought to be a key component of language, and various compositional benchmarks have been developed to empirically probe the compositional generalization of existing sequence processing models. These benchmarks often highlight failures of existing models, but it is not clear why these models fail in this way. In this paper, we seek to theoretically understand the role the compositional structure of the models plays in these failures and how this structure relates to their expressivity and sample complexity. We propose a general neuro-symbolic definition of compositional functions and their compositional complexity. We then show how various existing general and special purpose sequence processing models (such as recurrent, convolution and attention-based ones) fit this definition and use it to analyze their compositional complexity. Finally, we provide theoretical guarantees for the expressivity and systematic generalization of compositional models that explicitly depend on our proposed definition and highlighting factors which drive poor empirical performance.

Chitra Subramanian, Miao Liu, Naweed Khan et al.

Multi-agent reinforcement learning (MARL) is well-suited for runtime decision-making in optimizing the performance of systems where multiple agents coexist and compete for shared resources. However, applying common deep learning-based MARL solutions to real-world problems suffers from issues of interpretability, sample efficiency, partial observability, etc. To address these challenges, we present an event-driven formulation, where decision-making is handled by distributed co-operative MARL agents using neuro-symbolic methods. The recently introduced neuro-symbolic Logical Neural Networks (LNN) framework serves as a function approximator for the RL, to train a rules-based policy that is both logical and interpretable by construction. To enable decision-making under uncertainty and partial observability, we developed a novel probabilistic neuro-symbolic framework, Probabilistic Logical Neural Networks (PLNN), which combines the capabilities of logical reasoning with probabilistic graphical models. In PLNN, the upward/downward inference strategy, inherited from LNN, is coupled with belief bounds by setting the activation function for the logical operator associated with each neural network node to a probability-respecting generalization of the Fréchet inequalities. These PLNN nodes form the unifying element that combines probabilistic logic and Bayes Nets, permitting inference for variables with unobserved states. We demonstrate our contributions by addressing key MARL challenges for power sharing in a system-on-chip application.

Kyle Erwin, Guy Axelrod, Maria Chang et al.

The task of policy compliance detection (PCD) is to determine if a scenario is in compliance with respect to a set of written policies. In a conversational setting, the results of PCD can indicate if clarifying questions must be asked to determine compliance status. Existing approaches usually claim to have reasoning capabilities that are latent or require a large amount of annotated data. In this work, we propose logical decomposition for policy compliance (LDPC): a neuro-symbolic framework to detect policy compliance using large language models (LLMs) in a few-shot setting. By selecting only a few exemplars alongside recently developed prompting techniques, we demonstrate that our approach soundly reasons about policy compliance conversations by extracting sub-questions to be answered, assigning truth values from contextual information, and explicitly producing a set of logic statements from the given policies. The formulation of explicit logic graphs can in turn help answer PCDrelated questions with increased transparency and explainability. We apply this approach to the popular PCD and conversational machine reading benchmark, ShARC, and show competitive performance with no task-specific finetuning. We also leverage the inherently interpretable architecture of LDPC to understand where errors occur, revealing ambiguities in the ShARC dataset and highlighting the challenges involved with reasoning for conversational question answering.

Parikshit Ram, Kenneth L. Clarkson, Tim Klinger et al.

Various forms of sparse attention have been explored to mitigate the quadratic computational and memory cost of the attention mechanism in transformers. We study sparse transformers not through a lens of efficiency but rather in terms of learnability and generalization. Empirically studying a range of attention mechanisms, we find that input-dependent sparse attention models appear to converge faster and generalize better than standard attention models, while input-agnostic sparse attention models show no such benefits -- a phenomenon that is robust across architectural and optimization hyperparameter choices. This can be interpreted as demonstrating that concentrating a model's "semantic focus" with respect to the tokens currently being considered (in the form of input-dependent sparse attention) accelerates learning. We develop a theoretical characterization of the conditions that explain this behavior. We establish a connection between the stability of the standard softmax and the loss function's Lipschitz properties, then show how sparsity affects the stability of the softmax and the subsequent convergence and generalization guarantees resulting from the attention mechanism. This allows us to theoretically establish that input-agnostic sparse attention does not provide any benefits. We also characterize conditions when semantic focus (input-dependent sparse attention) can provide improved guarantees, and we validate that these conditions are in fact met in our empirical evaluations.

Alexander Gray, Noorhan Abbas

News recommendation is crucial for facilitating individuals' access to articles, particularly amid the increasingly digital landscape of news consumption. Consequently, extensive research is dedicated to News Recommender Systems (NRS) with increasingly sophisticated algorithms. Despite this sustained scholarly inquiry, there exists a notable research gap regarding the potential synergy achievable by amalgamating these algorithms to yield superior outcomes. This paper endeavours to address this gap by demonstrating how ensemble methods can be used to combine many diverse state-of-the-art algorithms to achieve superior results on the Microsoft News dataset (MIND). Additionally, we identify scenarios where ensemble methods fail to improve results and offer explanations for this occurrence. Our findings demonstrate that a combination of NRS algorithms can outperform individual algorithms, provided that the base learners are sufficiently diverse, with improvements of up to 5\% observed for an ensemble consisting of a content-based BERT approach and the collaborative filtering LSTUR algorithm. Additionally, our results demonstrate the absence of any improvement when combining insufficiently distinct methods. These findings provide insight into successful approaches of ensemble methods in NRS and advocates for the development of better systems through appropriate ensemble solutions.

Maxwell Crouse, Ramon Astudillo, Tahira Naseem et al.

We introduce Logical Offline Cycle Consistency Optimization (LOCCO), a scalable, semi-supervised method for training a neural semantic parser. Conceptually, LOCCO can be viewed as a form of self-learning where the semantic parser being trained is used to generate annotations for unlabeled text that are then used as new supervision. To increase the quality of annotations, our method utilizes a count-based prior over valid formal meaning representations and a cycle-consistency score produced by a neural text generation model as additional signals. Both the prior and semantic parser are updated in an alternate fashion from full passes over the training data, which can be seen as approximating the marginalization of latent structures through stochastic variational inference. The use of a count-based prior, frozen text generation model, and offline annotation process yields an approach with negligible complexity and latency increases as compared to conventional self-learning. As an added bonus, the annotations produced by LOCCO can be trivially repurposed to train a neural text generation model. We demonstrate the utility of LOCCO on the well-known WebNLG benchmark where we obtain an improvement of 2 points against a self-learning parser under equivalent conditions, an improvement of 1.3 points against the previous state-of-the-art parser, and competitive text generation performance in terms of BLEU score.

Daiki Kimura, Masaki Ono, Subhajit Chaudhury et al.

Deep reinforcement learning (RL) methods often require many trials before convergence, and no direct interpretability of trained policies is provided. In order to achieve fast convergence and interpretability for the policy in RL, we propose a novel RL method for text-based games with a recent neuro-symbolic framework called Logical Neural Network, which can learn symbolic and interpretable rules in their differentiable network. The method is first to extract first-order logical facts from text observation and external word meaning network (ConceptNet), then train a policy in the network with directly interpretable logical operators. Our experimental results show RL training with the proposed method converges significantly faster than other state-of-the-art neuro-symbolic methods in a TextWorld benchmark.

Sumit Neelam, Udit Sharma, Hima Karanam et al.

Knowledge Base Question Answering (KBQA) tasks that in-volve complex reasoning are emerging as an important re-search direction. However, most KBQA systems struggle withgeneralizability, particularly on two dimensions: (a) acrossmultiple reasoning types where both datasets and systems haveprimarily focused on multi-hop reasoning, and (b) across mul-tiple knowledge bases, where KBQA approaches are specif-ically tuned to a single knowledge base. In this paper, wepresent SYGMA, a modular approach facilitating general-izability across multiple knowledge bases and multiple rea-soning types. Specifically, SYGMA contains three high levelmodules: 1) KB-agnostic question understanding module thatis common across KBs 2) Rules to support additional reason-ing types and 3) KB-specific question mapping and answeringmodule to address the KB-specific aspects of the answer ex-traction. We demonstrate effectiveness of our system by evalu-ating on datasets belonging to two distinct knowledge bases,DBpedia and Wikidata. In addition, to demonstrate extensi-bility to additional reasoning types we evaluate on multi-hopreasoning datasets and a new Temporal KBQA benchmarkdataset on Wikidata, namedTempQA-WD1, introduced in thispaper. We show that our generalizable approach has bettercompetetive performance on multiple datasets on DBpediaand Wikidata that requires both multi-hop and temporal rea-soning

Haifeng Qian, Radu Marinescu, Alexander Gray et al.

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.

Prithviraj Sen, Breno W. S. R. Carvalho, Ibrahim Abdelaziz et al.

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.

Hang Jiang, Sairam Gurajada, Qiuhao Lu et al.

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.

Daiki Kimura, Subhajit Chaudhury, Akifumi Wachi et al.

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.

Francois Luus, Prithviraj Sen, Pavan Kapanipathi et al.

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.

Pavan Kapanipathi, Ibrahim Abdelaziz, Srinivas Ravishankar et al.

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.

Ryan Riegel, Alexander Gray, Francois Luus et al.

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.

Parikshit Ram, Sijia Liu, Deepak Vijaykeerthi et al.

The CASH problem has been widely studied in the context of automated configurations of machine learning (ML) pipelines and various solvers and toolkits are available. However, CASH solvers do not directly handle black-box constraints such as fairness, robustness or other domain-specific custom constraints. We present our recent approach [Liu, et al., 2020] that leverages the ADMM optimization framework to decompose CASH into multiple small problems and demonstrate how ADMM facilitates incorporation of black-box constraints.

Daniel Karl I. Weidele, Justin D. Weisz, Eno Oduor et al.

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.

Charu Aggarwal, Djallel Bouneffouf, Horst Samulowitz et al.

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.

Dakuo Wang, Justin D. Weisz, Michael Muller et al.

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.

Ravi Ganti, Alexander G. Gray

In this paper we propose a multi-armed bandit inspired, pool based active learning algorithm for the problem of binary classification. By carefully constructing an analogy between active learning and multi-armed bandits, we utilize ideas such as lower confidence bounds, and self-concordant regularization from the multi-armed bandit literature to design our proposed algorithm. Our algorithm is a sequential algorithm, which in each round assigns a sampling distribution on the pool, samples one point from this distribution, and queries the oracle for the label of this sampled point. The design of this sampling distribution is also inspired by the analogy between active learning and multi-armed bandits. We show how to derive lower confidence bounds required by our algorithm. Experimental comparisons to previously proposed active learning algorithms show superior performance on some standard UCI datasets.

Ravi Ganti, Alexander Gray

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.

Ryan R. Curtin, James R. Cline, N. P. Slagle et al.

MLPACK is a state-of-the-art, scalable, multi-platform C++ machine learning library released in late 2011 offering both a simple, consistent API accessible to novice users and high performance and flexibility to expert users by leveraging modern features of C++. MLPACK provides cutting-edge algorithms whose benchmarks exhibit far better performance than other leading machine learning libraries. MLPACK version 1.0.3, licensed under the LGPL, is available at http://www.mlpack.org.

Ryan R. Curtin, Parikshit Ram, Alexander G. Gray

The wide applicability of kernels makes the problem of max-kernel search ubiquitous and more general than the usual similarity search in metric spaces. We focus on solving this problem efficiently. We begin by characterizing the inherent hardness of the max-kernel search problem with a novel notion of directional concentration. Following that, we present a method to use an $O(n \log n)$ algorithm to index any set of objects (points in $\Real^\dims$ or abstract objects) directly in the Hilbert space without any explicit feature representations of the objects in this space. We present the first provably $O(\log n)$ algorithm for exact max-kernel search using this index. Empirical results for a variety of data sets as well as abstract objects demonstrate up to 4 orders of magnitude speedup in some cases. Extensions for approximate max-kernel search are also presented.

Nishant A. Mehta, Dongryeol Lee, Alexander G. Gray

Since its inception, the modus operandi of multi-task learning (MTL) has been to minimize the task-wise mean of the empirical risks. We introduce a generalized loss-compositional paradigm for MTL that includes a spectrum of formulations as a subfamily. One endpoint of this spectrum is minimax MTL: a new MTL formulation that minimizes the maximum of the tasks' empirical risks. Via a certain relaxation of minimax MTL, we obtain a continuum of MTL formulations spanning minimax MTL and classical MTL. The full paradigm itself is loss-compositional, operating on the vector of empirical risks. It incorporates minimax MTL, its relaxations, and many new MTL formulations as special cases. We show theoretically that minimax MTL tends to avoid worst case outcomes on newly drawn test tasks in the learning to learn (LTL) test setting. The results of several MTL formulations on synthetic and real problems in the MTL and LTL test settings are encouraging.

Dongryeol Lee, Alexander G. Gray

We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error control scheme integrating any arbitrary approximation method - within the best discretealgorithmic framework using adaptive hierarchical data structures. We rigorously evaluate these techniques empirically in the context of optimal bandwidth selection in kernel density estimation, revealing the strengths and weaknesses of current state-of-the-art approaches for the first time. Our results demonstrate that the new error control scheme yields improved performance, whereas the series expansion approach is only effective in low dimensions (five or less).

Michael P. Holmes, Alexander G. Gray, Charles Lee Isbell

Conditional density estimation generalizes regression by modeling a full density f(yjx) rather than only the expected value E(yjx). This is important for many tasks, including handling multi-modality and generating prediction intervals. Though fundamental and widely applicable, nonparametric conditional density estimators have received relatively little attention from statisticians and little or none from the machine learning community. None of that work has been applied to greater than bivariate data, presumably due to the computational difficulty of data-driven bandwidth selection. We describe the double kernel conditional density estimator and derive fast dual-tree-based algorithms for bandwidth selection using a maximum likelihood criterion. These techniques give speedups of up to 3.8 million in our experiments, and enable the first applications to previously intractable large multivariate datasets, including a redshift prediction problem from the Sloan Digital Sky Survey.

Hua Ouyang, Alexander Gray

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.

Nishant A. Mehta, Alexander G. Gray

The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task. Predictive sparse coding algorithms recently have demonstrated impressive performance on a variety of supervised tasks, but their generalization properties have not been studied. We establish the first generalization error bounds for predictive sparse coding, covering two settings: 1) the overcomplete setting, where the number of features k exceeds the original dimensionality d; and 2) the high or infinite-dimensional setting, where only dimension-free bounds are useful. Both learning bounds intimately depend on stability properties of the learned sparse encoder, as measured on the training sample. Consequently, we first present a fundamental stability result for the LASSO, a result characterizing the stability of the sparse codes with respect to perturbations to the dictionary. In the overcomplete setting, we present an estimation error bound that decays as \tilde{O}(sqrt(d k/m)) with respect to d and k. In the high or infinite-dimensional setting, we show a dimension-free bound that is \tilde{O}(sqrt(k^2 s / m)) with respect to k and s, where s is an upper bound on the number of non-zeros in the sparse code for any training data point.