Graph Neural Networks (GNNs) have been popularly used for analyzing non-Euclidean data such as social network data and biological data. Despite their success, the design of graph neural networks requires a lot of manual work and domain knowledge. In this paper, we propose a Graph Neural Architecture Search method (GraphNAS for short) that enables automatic search of the best graph neural architecture based on reinforcement learning. Specifically, GraphNAS first uses a recurrent network to generate variable-length strings that describe the architectures of graph neural networks, and then trains the recurrent network with reinforcement learning to maximize the expected accuracy of the generated architectures on a validation data set. Extensive experimental results on node classification tasks in both transductive and inductive learning settings demonstrate that GraphNAS can achieve consistently better performance on the Cora, Citeseer, Pubmed citation network, and protein-protein interaction network. On node classification tasks, GraphNAS can design a novel network architecture that rivals the best human-invented architecture in terms of test set accuracy.
This paper presents a novel approach for learning STRIPS action models from examples that compiles this inductive learning task into a classical planning task. Interestingly, the compilation approach is flexible to different amounts of available input knowledge; the learning examples can range from a set of plans (with their corresponding initial and final states) to just a pair of initial and final states (no intermediate action or state is given). Moreover, the compilation accepts partially specified action models and it can be used to validate whether the observation of a plan execution follows a given STRIPS action model, even if this model is not fully specified.
While physics conveys knowledge of nature built from an interplay between observations and theory, it has been considered less importantly in deep neural networks. Especially, there are few works leveraging physics behaviors when the knowledge is given less explicitly. In this work, we propose a novel architecture called Differentiable Physics-informed Graph Networks (DPGN) to incorporate implicit physics knowledge which is given from domain experts by informing it in latent space. Using the concept of DPGN, we demonstrate that climate prediction tasks are significantly improved. Besides the experiment results, we validate the effectiveness of the proposed module and provide further applications of DPGN, such as inductive learning and multistep predictions.
This work addresses the problem of reconstructing biomedical signals from their lower dimensional projections. Traditionally Compressed Sensing (CS) based techniques have been employed for this task. These are transductive inversion processes, the problem with these approaches is that the inversion is time-consuming and hence not suitable for real-time applications. With the recent advent of deep learning, Stacked Sparse Denoising Autoencoder (SSDAE) has been used for learning inversion in an inductive setup. The training period for inductive learning is large but is very fast during application -- capable of real-time speed. This work proposes a new approach for inductive learning of the inversion process. It is based on Coupled Analysis Dictionary Learning. Results on Biomedical signal reconstruction show that our proposed approach is very fast and yields result far better than CS and SSDAE.
Recurrent Neural Networks (RNNs) are theoretically Turing-complete and established themselves as a dominant model for language processing. Yet, there still remains an uncertainty regarding their language learning capabilities. In this paper, we empirically evaluate the inductive learning capabilities of Long Short-Term Memory networks, a popular extension of simple RNNs, to learn simple formal languages, in particular $a^nb^n$, $a^nb^nc^n$, and $a^nb^nc^nd^n$. We investigate the influence of various aspects of learning, such as training data regimes and model capacity, on the generalization to unobserved samples. We find striking differences in model performances under different training settings and highlight the need for careful analysis and assessment when making claims about the learning capabilities of neural network models.
We present Deep Graph Infomax (DGI), a general approach for learning node representations within graph-structured data in an unsupervised manner. DGI relies on maximizing mutual information between patch representations and corresponding high-level summaries of graphs---both derived using established graph convolutional network architectures. The learnt patch representations summarize subgraphs centered around nodes of interest, and can thus be reused for downstream node-wise learning tasks. In contrast to most prior approaches to unsupervised learning with GCNs, DGI does not rely on random walk objectives, and is readily applicable to both transductive and inductive learning setups. We demonstrate competitive performance on a variety of node classification benchmarks, which at times even exceeds the performance of supervised learning.
In recent years, non-monotonic Inductive Logic Programming has received growing interest. Specifically, several new learning frameworks and algorithms have been introduced for learning under the answer set semantics, allowing the learning of common-sense knowledge involving defaults and exceptions, which are essential aspects of human reasoning. In this paper, we present a noise-tolerant generalisation of the learning from answer sets framework. We evaluate our ILASP3 system, both on synthetic and on real datasets, represented in the new framework. In particular, we show that on many of the datasets ILASP3 achieves a higher accuracy than other ILP systems that have previously been applied to the datasets, including a recently proposed differentiable learning framework.
Convolutional neural networks (CNNs) have achieved great success on grid-like data such as images, but face tremendous challenges in learning from more generic data such as graphs. In CNNs, the trainable local filters enable the automatic extraction of high-level features. The computation with filters requires a fixed number of ordered units in the receptive fields. However, the number of neighboring units is neither fixed nor are they ordered in generic graphs, thereby hindering the applications of convolutional operations. Here, we address these challenges by proposing the learnable graph convolutional layer (LGCL). LGCL automatically selects a fixed number of neighboring nodes for each feature based on value ranking in order to transform graph data into grid-like structures in 1-D format, thereby enabling the use of regular convolutional operations on generic graphs. To enable model training on large-scale graphs, we propose a sub-graph training method to reduce the excessive memory and computational resource requirements suffered by prior methods on graph convolutions. Our experimental results on node classification tasks in both transductive and inductive learning settings demonstrate that our methods can achieve consistently better performance on the Cora, Citeseer, Pubmed citation network, and protein-protein interaction network datasets. Our results also indicate that the proposed methods using sub-graph training strategy are more efficient as compared to prior approaches.
In recent years a number of large-scale triple-oriented knowledge graphs have been generated and various models have been proposed to perform learning in those graphs. Most knowledge graphs are static and reflect the world in its current state. In reality, of course, the state of the world is changing: a healthy person becomes diagnosed with a disease and a new president is inaugurated. In this paper, we extend models for static knowledge graphs to temporal knowledge graphs. This enables us to store episodic data and to generalize to new facts (inductive learning). We generalize leading learning models for static knowledge graphs (i.e., Tucker, RESCAL, HolE, ComplEx, DistMult) to temporal knowledge graphs. In particular, we introduce a new tensor model, ConT, with superior generalization performance. The performances of all proposed models are analyzed on two different datasets: the Global Database of Events, Language, and Tone (GDELT) and the database for Integrated Conflict Early Warning System (ICEWS). We argue that temporal knowledge graph embeddings might be models also for cognitive episodic memory (facts we remember and can recollect) and that a semantic memory (current facts we know) can be generated from episodic memory by a marginalization operation. We validate this episodic-to-semantic projection hypothesis with the ICEWS dataset.
The objective of this paper is to propose a method that will generate a causal explanation of observed events in an uncertain world and then make decisions based on that explanation. Feedback can cause the explanation and decisions to be modified. I call the method Theory-Based Inductive Learning (T-BIL). T-BIL integrates deductive learning, based on a technique called Explanation-Based Generalization (EBG) from the field of machine learning, with inductive learning methods from Bayesian decision theory. T-BIL takes as inputs (1) a decision problem involving a sequence of related decisions over time, (2) a training example of a solution to the decision problem in one period, and (3) the domain theory relevant to the decision problem. T-BIL uses these inputs to construct a probabilistic explanation of why the training example is an instance of a solution to one stage of the sequential decision problem. This explanation is then generalized to cover a more general class of instances and is used as the basis for making the next-stage decisions. As the outcomes of each decision are observed, the explanation is revised, which in turn affects the subsequent decisions. A detailed example is presented that uses T-BIL to solve a very general stochastic adaptive control problem for an autonomous mobile robot.
Knowledge Representation and Reasoning and Machine Learning are two important fields in AI. Nonmonotonic logic programming (NMLP) and Answer Set Programming (ASP) provide formal languages for representing and reasoning with commonsense knowledge and realize declarative problem solving in AI. On the other side, Inductive Logic Programming (ILP) realizes Machine Learning in logic programming, which provides a formal background to inductive learning and the techniques have been applied to the fields of relational learning and data mining. Generally speaking, NMLP and ASP realize nonmonotonic reasoning while lack the ability of learning. By contrast, ILP realizes inductive learning while most techniques have been developed under the classical monotonic logic. With this background, some researchers attempt to combine techniques in the context of nonmonotonic ILP. Such combination will introduce a learning mechanism to programs and would exploit new applications on the NMLP side, while on the ILP side it will extend the representation language and enable us to use existing solvers. Cross-fertilization between learning and nonmonotonic reasoning can also occur in such as the use of answer set solvers for ILP, speed-up learning while running answer set solvers, learning action theories, learning transition rules in dynamical systems, abductive learning, learning biological networks with inhibition, and applications involving default and negation. This workshop is the first attempt to provide an open forum for the identification of problems and discussion of possible collaborations among researchers with complementary expertise. The workshop was held on September 15th of 2013 in Corunna, Spain. This post-proceedings contains five technical papers (out of six accepted papers) and the abstract of the invited talk by Luc De Raedt.
Event recognition systems rely on properly engineered knowledge bases of event definitions to infer occurrences of events in time. The manual development of such knowledge is a tedious and error-prone task, thus event-based applications may benefit from automated knowledge construction techniques, such as Inductive Logic Programming (ILP), which combines machine learning with the declarative and formal semantics of First-Order Logic. However, learning temporal logical formalisms, which are typically utilized by logic-based Event Recognition systems is a challenging task, which most ILP systems cannot fully undertake. In addition, event-based data is usually massive and collected at different times and under various circumstances. Ideally, systems that learn from temporal data should be able to operate in an incremental mode, that is, revise prior constructed knowledge in the face of new evidence. Most ILP systems are batch learners, in the sense that in order to account for new evidence they have no alternative but to forget past knowledge and learn from scratch. Given the increased inherent complexity of ILP and the volumes of real-life temporal data, this results to algorithms that scale poorly. In this work we present an incremental method for learning and revising event-based knowledge, in the form of Event Calculus programs. The proposed algorithm relies on abductive-inductive learning and comprises a scalable clause refinement methodology, based on a compressive summarization of clause coverage in a stream of examples. We present an empirical evaluation of our approach on real and synthetic data from activity recognition and city transport applications.
This paper presents an idea of inductive learning use for rule generation from ontologies. The main purpose of the paper is to evaluate the possibility of inductive learning use in rule generation from ontologies and to develop the way how this can be done. Generated rules are necessary to supplement or even to develop the Semantic Web Expert System (SWES) knowledge base. The SWES emerges as the result of evolution of expert system concept toward the Web, and the SWES is based on the Semantic Web technologies. Available publications show that the problem of rule generation from ontologies based on inductive learning is not investigated deeply enough.
Transductive learning considers a training set of $m$ labeled samples and a test set of $u$ unlabeled samples, with the goal of best labeling that particular test set. Conversely, inductive learning considers a training set of $m$ labeled samples drawn iid from $P(X,Y)$, with the goal of best labeling any future samples drawn iid from $P(X)$. This comparison suggests that transduction is a much easier type of inference than induction, but is this really the case? This paper provides a negative answer to this question, by proving the first known minimax lower bounds for transductive, realizable, binary classification. Our lower bounds show that $m$ should be at least $\Omega(d/\epsilon + \log(1/\delta)/\epsilon)$ when $\epsilon$-learning a concept class $\mathcal{H}$ of finite VC-dimension $d<\infty$ with confidence $1-\delta$, for all $m \leq u$. This result draws three important conclusions. First, general transduction is as hard as general induction, since both problems have $\Omega(d/m)$ minimax values. Second, the use of unlabeled data does not help general transduction, since supervised learning algorithms such as ERM and (Hanneke, 2015) match our transductive lower bounds while ignoring the unlabeled test set. Third, our transductive lower bounds imply lower bounds for semi-supervised learning, which add to the important discussion about the role of unlabeled data in machine learning.
Objects or structures that are regular take uniform dimensions. Based on the concepts of regular models, our previous research work has developed a system of a regular ontology that models learning structures in a multiagent system for uniform pre-assessments in a learning environment. This regular ontology has led to the modelling of a classified rules learning algorithm that predicts the actual number of rules needed for inductive learning processes and decision making in a multiagent system. But not all processes or models are regular. Thus this paper presents a system of polynomial equation that can estimate and predict the required number of rules of a non-regular ontology model given some defined parameters.
Formal synthesis is the process of generating a program satisfying a high-level formal specification. In recent times, effective formal synthesis methods have been proposed based on the use of inductive learning. We refer to this class of methods that learn programs from examples as formal inductive synthesis. In this paper, we present a theoretical framework for formal inductive synthesis. We discuss how formal inductive synthesis differs from traditional machine learning. We then describe oracle-guided inductive synthesis (OGIS), a framework that captures a family of synthesizers that operate by iteratively querying an oracle. An instance of OGIS that has had much practical impact is counterexample-guided inductive synthesis (CEGIS). We present a theoretical characterization of CEGIS for learning any program that computes a recursive language. In particular, we analyze the relative power of CEGIS variants where the types of counterexamples generated by the oracle varies. We also consider the impact of bounded versus unbounded memory available to the learning algorithm. In the special case where the universe of candidate programs is finite, we relate the speed of convergence to the notion of teaching dimension studied in machine learning theory. Altogether, the results of the paper take a first step towards a theoretical foundation for the emerging field of formal inductive synthesis.
Use of computational methods to predict gene regulatory networks (GRNs) from gene expression data is a challenging task. Many studies have been conducted using unsupervised methods to fulfill the task; however, such methods usually yield low prediction accuracies due to the lack of training data. In this article, we propose semi-supervised methods for GRN prediction by utilizing two machine learning algorithms, namely support vector machines (SVM) and random forests (RF). The semi-supervised methods make use of unlabeled data for training. We investigate inductive and transductive learning approaches, both of which adopt an iterative procedure to obtain reliable negative training data from the unlabeled data. We then apply our semi-supervised methods to gene expression data of Escherichia coli and Saccharomyces cerevisiae, and evaluate the performance of our methods using the expression data. Our analysis indicated that the transductive learning approach outperformed the inductive learning approach for both organisms. However, there was no conclusive difference identified in the performance of SVM and RF. Experimental results also showed that the proposed semi-supervised methods performed better than existing supervised methods for both organisms.
In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the classical setting, from a simple independence requirement with a physical interpretation of being non-signalling. Thus, two seemingly different definitions of inductive learning happen to coincide. This follows from the properties of classical information that break down in the quantum setup. We prove a quantum de Finetti theorem for quantum channels, which shows that in the quantum case, the equivalence holds in the asymptotic setting, that is, for large number of test instances. This reveals a natural analogy between classical learning protocols and their quantum counterparts, justifying a similar treatment, and allowing to inquire about standard elements in computational learning theory, such as structural risk minimization and sample complexity.
Random walks are at the heart of many existing deep learning algorithms for graph data. However, such algorithms have many limitations that arise from the use of random walks, e.g., the features resulting from these methods are unable to transfer to new nodes and graphs as they are tied to node identity. In this work, we introduce the notion of attributed random walks which serves as a basis for generalizing existing methods such as DeepWalk, node2vec, and many others that leverage random walks. Our proposed framework enables these methods to be more widely applicable for both transductive and inductive learning as well as for use on graphs with attributes (if available). This is achieved by learning functions that generalize to new nodes and graphs. We show that our proposed framework is effective with an average AUC improvement of 16.1% while requiring on average 853 times less space than existing methods on a variety of graphs from several domains.
When humans perform inductive learning, they often enhance the process with background knowledge. With the increasing availability of well-formed collaborative knowledge bases, the performance of learning algorithms could be significantly enhanced if a way were found to exploit these knowledge bases. In this work, we present a novel algorithm for injecting external knowledge into induction algorithms using feature generation. Given a feature, the algorithm defines a new learning task over its set of values, and uses the knowledge base to solve the constructed learning task. The resulting classifier is then used as a new feature for the original problem. We have applied our algorithm to the domain of text classification using large semantic knowledge bases. We have shown that the generated features significantly improve the performance of existing learning algorithms.