Systems for symbolic event recognition infer occurrences of events in time using a set of event definitions in the form of first-order rules. The Event Calculus is a temporal logic that has been used as a basis in event recognition applications, providing among others, direct connections to machine learning, via Inductive Logic Programming (ILP). We present an ILP system for online learning of Event Calculus theories. To allow for a single-pass learning strategy, we use the Hoeffding bound for evaluating clauses on a subset of the input stream. We employ a decoupling scheme of the Event Calculus axioms during the learning process, that allows to learn each clause in isolation. Moreover, we use abductive-inductive logic programming techniques to handle unobserved target predicates. We evaluate our approach on an activity recognition application and compare it to a number of batch learning techniques. We obtain results of comparable predicative accuracy with significant speed-ups in training time. We also outperform hand-crafted rules and match the performance of a sound incremental learner that can only operate on noise-free datasets. This paper is under consideration for acceptance in TPLP.
The Hoeffding bound has been used for propositional machine learning tasks on data streams, such as learning decision trees @cite_0 and decision rules @cite_21 , and clustering @cite_15 . However, its usage for learning relational models is limited. One reason is that it requires independence of observations, which cannot always be ensured in relational domains, due to dependencies in the data @cite_5 @cite_19 @cite_11 @cite_22 . An ILP approach that uses the Hoeffding bound for relational learning is @cite_20 , an extension of the system for learning first-order decision trees @cite_25 . These are decision trees where each internal node consists of a conjunction of literals and each leaf is a propositional predicate representing a class. constructs trees by testing conjunctions of literals at each node, using an ILP refinement operator to generate the conjunctions and information gain as the guiding heuristic. extends by using the Hoeffding bound to perform these internal tests on a subset of the training data. To ensure independence of observations, learns from interpretations @cite_18 , a setting, used also by , where each training instance is assumed a disconnected part of the dataset.
@cite_18 @cite_22 @cite_21 @cite_0 @cite_19 @cite_5 @cite_15 @cite_25 @cite_20 @cite_11
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In mining data streams the most popular tool is the Hoeffding tree algorithm. It uses the Hoeffding's bound to determine the smallest number of examples needed at a node to select a splitting attribute. In the literature the same Hoeffding's bound was used for any evaluation function (heuristic measure), e.g., information gain or Gini index. In this paper, it is shown that the Hoeffding's inequality is not appropriate to solve the underlying problem. We prove two theorems presenting the McDiarmid's bound for both the information gain, used in ID3 algorithm, and for Gini index, used in Classification and Regression Trees (CART) algorithm. The results of the paper guarantee that a decision tree learning system, applied to data streams and based on the McDiarmid's bound, has the property that its output is nearly identical to that of a conventional learner. The results of the paper have a great impact on the state of the art of mining data streams and various developed so far methods and algorithms should be reconsidered. Abstract The emergence of ubiquitous sources of streaming data has given rise to the popularity of algorithms for online machine learning. In that context, Hoeffding trees represent the state-of-the-art algorithms for online classification. Their popularity stems in large part from their ability to process large quantities of data with a speed that goes beyond the processing power of any other streaming or batch learning algorithm. As a consequence, Hoeffding trees have often been used as base models of many ensemble learning algorithms for online classification. However, despite the existence of many algorithms for online classification, ensemble learning algorithms for online regression do not exist. In particular, the field of online any-time regression analysis seems to have experienced a serious lack of attention. In this paper, we address this issue through a study and an empirical evaluation of a set of online algorithms for regression, which includes the baseline Hoeffding-based regression trees, online option trees, and an online least mean squares filter. We also design, implement and evaluate two novel ensemble learning methods for online regression: online bagging with Hoeffding-based model trees, and an online RandomForest method in which we have used a randomized version of the online model tree learning algorithm as a basic building block. Within the study presented in this paper, we evaluate the proposed algorithms along several dimensions: predictive accuracy and quality of models, time and memory requirements, bias–variance and bias–variance–covariance decomposition of the error, and responsiveness to concept drift. Relational learning can be described as the task of learning first-order logic rules from examples. It has enabled a number of new machine learning applications, e.g. graph mining and link analysis. Inductive Logic Programming (ILP) performs relational learning either directly by manipulating first-order rules or through propositionalization, which translates the relational task into an attribute-value learning task by representing subsets of relations as features. In this paper, we introduce a fast method and system for relational learning based on a novel propositionalization called Bottom Clause Propositionalization (BCP). Bottom clauses are boundaries in the hypothesis search space used by ILP systems Progol and Aleph. Bottom clauses carry semantic meaning and can be mapped directly onto numerical vectors, simplifying the feature extraction process. We have integrated BCP with a well-known neural-symbolic system, C-IL2P, to perform learning from numerical vectors. C-IL2P uses background knowledge in the form of propositional logic programs to build a neural network. The integrated system, which we call CILP++, handles first-order logic knowledge and is available for download from Sourceforge. We have evaluated CILP++ on seven ILP datasets, comparing results with Aleph and a well-known propositionalization method, RSD. The results show that CILP++ can achieve accuracy comparable to Aleph, while being generally faster, BCP achieved statistically significant improvement in accuracy in comparison with RSD when running with a neural network, but BCP and RSD perform similarly when running with C4.5. We have also extended CILP++ to include a statistical feature selection method, mRMR, with preliminary results indicating that a reduction of more than 90 of features can be achieved with a small loss of accuracy. Nowadays, many organizations have relational databases with millions of records and an important question is how to extract information from them. This work proposes HTILDE (Hoeffding TILDE) to handle very large relational databases, based on the Inductive Logic Programming (ILP) system TILDE (Top-down Induction of Logical Decision Trees) and the propositional Very Fast Decision Tree (VFDT) learner. It is an incremental and anytime algorithm that uses the Hoeffding bound to find out the amount of examples that must be considered for choosing the best test for a node. The results show that, compared to TILDE, HTILDE generates theories from very large relational datasets more efficiently without harming their quality measures (F-measure, precision, recall and accuracy). Also, HTILDE learns less complex theories than TILDE. We study resource-limited online learning, motivated by the problem of conditional-branch outcome prediction in computer architecture. In particular, we consider (parallel) time and space-efficient ensemble learners for online settings, empirically demonstrating benefits similar to those shown previously for offline ensembles. Our learning algorithms are inspired by the previously published “boosting by filtering” framework as well as the offline Arc-x4 boosting-style algorithm. We train ensembles of online decision trees using a novel variant of the ID4 online decision-tree algorithm as the base learner, and show empirical results for both boosting and bagging-style online ensemble methods. Our results evaluate these methods on both our branch prediction domain and online variants of three familiar machine-learning benchmarks. Our data justifies three key claims. First, we show empirically that our extensions to ID4 significantly improve performance for single trees and additionally are critical to achieving performance gains in tree ensembles. Second, our results indicate significant improvements in predictive accuracy with ensemble size for the boosting-style algorithm. The bagging algorithms we tried showed poor performance relative to the boosting-style algorithm (but still improve upon individual base learners). Third, we show that ensembles of small trees are often able to outperform large single trees with the same number of nodes (and similarly outperform smaller ensembles of larger trees that use the same total number of nodes). This makes online boosting particularly useful in domains such as branch prediction with tight space restrictions (i.e., the available real-estate on a microprocessor chip). When comparing inductive logic programming (ILP) and attribute-value learning techniques, there is a trade-off between expressive power and efficiency. Inductive logic programming techniques are typically more expressive but also less efficient. Therefore, the data sets handled by current inductive logic programming systems are small according to general standards within the data mining community. The main source of inefficiency lies in the assumption that several examples may be related to each other, so they cannot be handled independently. Within the learning from interpretations framework for inductive logic programming this assumption is unnecessary, which allows to scale up existing ILP algorithms. In this paper we explain this learning setting in the context of relational databases. We relate the setting to propositional data mining and to the classical ILP setting, and show that learning from interpretations corresponds to learning from multiple relations and thus extends the expressiveness of propositional learning, while maintaining its efficiency to a large extent (which is not the case in the classical ILP setting). As a case study, we present two alternative implementations of the ILP system TILDE (Top-down Induction of Logical DEcision trees): TILDEclassic, which loads all data in main memory, and TILDELDS, which loads the examples one by one. We experimentally compare the implementations, showing TILDELDS can handle large data sets (in the order of 100,000 examples or 100 MB) and indeed scales up linearly in the number of examples. Many interesting domains in machine learning can be viewed as networks, with relationships (e.g., friendships) connecting items (e.g., individuals). The Active Exploration (AE) task is to identify all items in a network with a desired trait (i.e., positive labels) given only partial information about the network. The AE process iteratively queries for labels or network structure within a limited budget; thus, accurate predictions prior to making each query is critical to maximizing the number of positives gathered. However, the targeted AE query process produces partially observed networks that can create difficulties for predictive modeling. In particular, we demonstrate that these partial networks can exhibit extreme label correlation bias, which makes it difficult for conventional relational learning methods to accurately estimate relational parameters. To overcome this issue, we model the joint distribution of possible edges and labels to improve learning and inference. Our proposed method, Probabilistic Relational Expectation Maximization (PR-EM), is the first AE approach to accurately learn the complex dependencies between attributes, labels, and structure to improve predictions. PR-EM utilizes collective inference over the missing relationships in the partial network to jointly infer unknown item traits. Further, we develop a linear inference algorithm to facilitate efficient use of PR-EM in large networks. We test our approach on four real world networks, showing that AE with PR-EM gathers significantly more positive items compared to state-of-the-art methods. Many stream classification algorithms use the Hoeffding Inequality to identify the best split attribute during tree induction. We show that the prerequisites of the Inequality are violated by these algorithms, and we propose corrective steps. The new stream classification core, correctedVFDT , satisfies the prerequisites of the Hoeffding Inequality and thus provides the expected performance guarantees. The goal of our work is not to improve accuracy, but to guarantee a reliable and interpretable error bound. Nonetheless, we show that our solution achieves lower error rates regarding split attributes and sooner split decisions while maintaining a similar level of accuracy. We prove new upper and lower bounds on the sample complexity of (a#x03B5;, a#x03B4;) differentially private algorithms for releasing approximate answers to threshold functions. A threshold function cx over a totally ordered domain X evaluates to cx(y) = 1 if y a#x2264; x, and evaluates to 0 otherwise. We give the first nontrivial lower bound for releasing thresholds with (a#x03B5;, a#x03B4;) differential privacy, showing that the task is impossible over an infinite domain X, and moreover requires sample complexity n a#x2265; (log* |X|), which grows with the size of the domain. Inspired by the techniques used to prove this lower bound, we give an algorithm for releasing thresholds with n a#x2264; 2(1+o(1)) log* |X| samples. This improves the previous best upper bound of 8(1+o(1)) log* |X| (, RANDOM'13). Our sample complexity upper and lower bounds also apply to the tasks of learning distributions with respect to Kolmogorov distance and of properly PAC learning thresholds with differential privacy. The lower bound gives the first separation between the sample complexity of properly learning a concept class with (a#x03B5;, a#x03B4;) differential privacy and learning without privacy. For properly learning thresholds in 'dimensions, this lower bound extends to n a#x2265; (l a#x2219; log* |X|). To obtain our results, we give reductions in both directions from releasing and properly learning thresholds and the simpler interior point problem. Given a database D of elements from X, the interior point problem asks for an element between the smallest and largest elements in D. We introduce new recursive constructions for bounding the sample complexity of the interior point problem, as well as further reductions and techniques for proving impossibility results for other basic problems in differential privacy. This paper introduces a framework for inference of timed temporal logic properties from data. The dataset is given as a finite set of pairs of finite-time system traces and labels, where the labels indicate whether the traces exhibit some desired behavior (e.g., a ship traveling along a safe route). We propose a decision-tree based approach for learning signal temporal logic classifiers. The method produces binary decision trees that represent the inferred formulae. Each node of the tree contains a test associated with the satisfaction of a simple formula, optimally tuned from a predefined finite set of primitives. Optimality is assessed using heuristic impurity measures, which capture how well the current primitive splits the data with respect to the traces' labels. We propose extensions of the usual impurity measures from machine learning literature to handle classification of system traces by leveraging upon the robustness degree concept. The proposed incremental construction procedure greatly improves the execution time and the accuracy compared to existing algorithms. We present two case studies that illustrate the usefulness and the computational advantages of the algorithms. The first is an anomaly detection problem in a maritime environment. The second is a fault detection problem in an automotive powertrain system. Knowledge base (KB) completion adds new facts to a KB by making inferences from existing facts, for example by inferring with high likelihood nationality(X,Y) from bornIn(X,Y). Most previous methods infer simple one-hop relational synonyms like this, or use as evidence a multi-hop relational path treated as an atomic feature, like bornIn(X,Z) -> containedIn(Z,Y). This paper presents an approach that reasons about conjunctions of multi-hop relations non-atomically, composing the implications of a path using a recursive neural network (RNN) that takes as inputs vector embeddings of the binary relation in the path. Not only does this allow us to generalize to paths unseen at training time, but also, with a single high-capacity RNN, to predict new relation types not seen when the compositional model was trained (zero-shot learning). We assemble a new dataset of over 52M relational triples, and show that our method improves over a traditional classifier by 11 , and a method leveraging pre-trained embeddings by 7 . Attribute-value based representations, standard in today's data mining systems, have a limited expressiveness. Inductive Logic Programming provides an interesting alternative, particularly for learning from structured examples whose parts, each with its own attributes, are related to each other by means of first-order predicates. Several subsets of first-order logic (FOL) with different expressive power have been proposed in Inductive Logic Programming (ILP). The challenge lies in the fact that the more expressive the subset of FOL the learner works with, the more critical the dimensionality of the learning task. The Datalog language is expressive enough to represent realistic learning problems when data is given directly in a relational database, making it a suitable tool for data mining. Consequently, it is important to elaborate techniques that will dynamically decrease the dimensionality of learning tasks expressed in Datalog, just as Feature Subset Selection (FSS) techniques do it in attribute-value learning. The idea of re-using these techniques in ILP runs immediately into a problem as ILP examples have variable size and do not share the same set of literals. We propose here the first paradigm that brings Feature Subset Selection to the level of ILP, in languages at least as expressive as Datalog. The main idea is to first perform a change of representation, which approximates the original relational problem by a multi-instance problem. The representation obtained as the result is suitable for FSS techniques which we adapted from attribute-value learning by taking into account some of the characteristics of the data due to the change of representation. We present the simple FSS proposed for the task, the requisite change of representation, and the entire method combining those two algorithms. The method acts as a filter, preprocessing the relational data, prior to the model building, which outputs relational examples with empirically relevant literals. We discuss experiments in which the method was successfully applied to two real-world domains. This article considers approaches which rerank the output of an existing probabilistic parser. The base parser produces a set of candidate parses for each input sentence, with associated probabilities that define an initial ranking of these parses. A second model then attempts to improve upon this initial ranking, using additional features of the tree as evidence. The strength of our approach is that it allows a tree to be represented as an arbitrary set of features, without concerns about how these features interact or overlap and without the need to define a derivation or a generative model which takes these features into account. We introduce a new method for the reranking task, based on the boosting approach to ranking problems described in (1998). We apply the boosting method to parsing the Wall Street Journal treebank. The method combined the log-likelihood under a baseline model (that of Collins [1999]) with evidence from an additional 500,000 features over parse trees that were not included in the original model. The new model achieved 89.75 F-measure, a 13 relative decrease in F measure error over the baseline model's score of 88.2 . The article also introduces a new algorithm for the boosting approach which takes advantage of the sparsity of the feature space in the parsing data. Experiments show significant efficiency gains for the new algorithm over the obvious implementation of the boosting approach. We argue that the method is an appealing alternative—in terms of both simplicity and efficiency—to work on feature selection methods within log-linear (maximum-entropy) models. Although the experiments in this article are on natural language parsing (NLP), the approach should be applicable to many other NLP problems which are naturally framed as ranking tasks, for example, speech recognition, machine translation, or natural language generation. Mining of data streams must balance three evaluation dimensions: accuracy, time and memory Excellent accuracy on data streams has been obtained with Naive Bayes Hoeffding Trees—Hoeffding Trees with naive Bayes models at the leaf nodes—albeit with increased runtime compared to standard Hoeffding Trees In this paper, we show that runtime can be reduced by replacing naive Bayes with perceptron classifiers, while maintaining highly competitive accuracy We also show that accuracy can be increased even further by combining majority vote, naive Bayes, and perceptrons We evaluate four perceptron-based learning strategies and compare them against appropriate baselines: simple perceptrons, Perceptron Hoeffding Trees, hybrid Naive Bayes Perceptron Trees, and bagged versions thereof We implement a perceptron that uses the sigmoid activation function instead of the threshold activation function and optimizes the squared error, with one perceptron per class value We test our methods by performing an evaluation study on synthetic and real-world datasets comprising up to ten million examples. Recommending phrases from web pages for advertisers to bid on against search engine queries is an important research problem with direct commercial impact. Most approaches have found it infeasible to determine the relevance of all possible queries to a given ad landing page and have focussed on making recommendations from a small set of phrases extracted (and expanded) from the page using NLP and ranking based techniques. In this paper, we eschew this paradigm, and demonstrate that it is possible to efficiently predict the relevant subset of queries from a large set of monetizable ones by posing the problem as a multi-label learning task with each query being represented by a separate label. We develop Multi-label Random Forests to tackle problems with millions of labels. Our proposed classifier has prediction costs that are logarithmic in the number of labels and can make predictions in a few milliseconds using 10 Gb of RAM. We demonstrate that it is possible to generate training data for our classifier automatically from click logs without any human annotation or intervention. We train our classifier on tens of millions of labels, features and training points in less than two days on a thousand node cluster. We develop a sparse semi-supervised multi-label learning formulation to deal with training set biases and noisy labels harvested automatically from the click logs. This formulation is used to infer a belief in the state of each label for each training ad and the random forest classifier is extended to train on these beliefs rather than the given labels. Experiments reveal significant gains over ranking and NLP based techniques on a large test set of 5 million ads using multiple metrics. Very Fast Decision Tree (VFDT) in data stream mining has been widely studied for more than a decade. VFDT in essence can mine over a portion of an unbounded data stream at a time, and the structure of the decision tree gets updated whenever new data feed in; hence it can predict better upon the input of fresh data. Inherent from traditional decision trees that use information gains for tree induction, VFDT may suffer the same over-fitting problem where noise in the training data leads to excessive tree branches therefore decline in prediction accuracy. This problem is aggravated in stream mining because limited run-time memory (for storing the whole decision tree) and reasonable accuracy are often the criteria for implementing VFDT. Post-pruning that was a popular technique used in traditional decision tree to keep the tree size in check, however may not be applicable for VFDT in situ. In this paper a new model that extends from VFDT called Optimized VFDT is proposed, for controlling the tree size while sustaining good prediction accuracy. This is enabled by using an adaptive threshold tie and incremental pruning in tree induction. Experimental results show that an optimal ratio of tree size and accuracy can be achieved by OVFDT. Most current statistical natural language processing models use only local features so as to permit dynamic programming in inference, but this makes them unable to fully account for the long distance structure that is prevalent in language use. We show how to solve this dilemma with Gibbs sampling, a simple Monte Carlo method used to perform approximate inference in factored probabilistic models. By using simulated annealing in place of Viterbi decoding in sequence models such as HMMs, CMMs, and CRFs, it is possible to incorporate non-local structure while preserving tractable inference. We use this technique to augment an existing CRF-based information extraction system with long-distance dependency models, enforcing label consistency and extraction template consistency constraints. This technique results in an error reduction of up to 9 over state-of-the-art systems on two established information extraction tasks. We present an algorithm for the statistical learning setting with a bounded exp-concave loss in @math dimensions that obtains excess risk @math with probability at least @math . The core technique is to boost the confidence of recent in-expectation @math excess risk bounds for empirical risk minimization (ERM), without sacrificing the rate, by leveraging a Bernstein condition which holds due to exp-concavity. We also show that with probability @math the standard ERM method obtains excess risk @math . We further show that a regret bound for any online learner in this setting translates to a high probability excess risk bound for the corresponding online-to-batch conversion of the online learner. Lastly, we present two high probability bounds for the exp-concave model selection aggregation problem that are quantile-adaptive in a certain sense. The first bound is a purely exponential weights type algorithm, obtains a nearly optimal rate, and has no explicit dependence on the Lipschitz continuity of the loss. The second bound requires Lipschitz continuity but obtains the optimal rate. Breiman (2001a,b) has recently developed an ensemble classification and regression approach that displayed outstanding performance with regard prediction error on a suite of benchmark datasets. As the base constituents of the ensemble are tree-structured predictors, and since each of these is constructed using an injection of randomness, the method is called ‘random forests’. That the exceptional performance is attained with seemingly only a single tuning parameter, to which sensitivity is minimal, makes the methodology all the more remarkable. The individual trees comprising the forest are all grown to maximal depth. While this helps with regard bias, there is the familiar tradeoff with variance. However, these variability concerns were potentially obscured because of an interesting feature of those benchmarking datasets extracted from the UCI machine learning repository for testing: all these datasets are hard to overfit using tree-structured methods. This raises issues about the scope of the repository. With this as motivation, and coupled with experience from boosting methods, we revisit the formulation of random forests and investigate prediction performance on real-world and simulated datasets for which maximally sized trees do overfit. These explorations reveal that gains can be realized by additional tuning to regulate tree size via limiting the number of splits and or the size of nodes for which splitting is allowed. Nonetheless, even in these settings, good performance for random forests can be attained by using larger (than default) primary tuning parameter values. Abstract Visual tracking algorithms based on structured output support vector machine (SOSVM) have demonstrated excellent performance. However, sampling methods and optimization strategies of SOSVM undesirably increase the computational overloads, which hinder real-time application of these algorithms. Moreover, due to the lack of high-dimensional features and dense training samples, SOSVM-based algorithms are unstable to deal with various challenging scenarios, such as occlusions and scale variations. Recently, visual tracking algorithms based on discriminative correlation filters (DCF), especially the combination of DCF and features from deep convolutional neural networks (CNN), have been successfully applied to visual tracking, and attains surprisingly good performance on recent benchmarks. The success is mainly attributed to two aspects: the circular correlation properties of DCF and the powerful representation capabilities of CNN features. Nevertheless, compared with SOSVM, DCF-based algorithms are restricted to simple ridge regression which has a weaker discriminative ability. In this paper, a novel circular and structural operator tracker (CSOT) is proposed for high performance visual tracking, it not only possesses the powerful discriminative capability of SOSVM but also efficiently inherits the superior computational efficiency of DCF. Based on the proposed circular and structural operators, a set of primal confidence score maps can be obtained by circular correlating feature maps with their corresponding structural correlation filters. Furthermore, an implicit interpolation is applied to convert the multi-resolution feature maps to the continuous domain and make all primal confidence score maps have the same spatial resolution. Then, we exploit an efficient ensemble post-processor based on relative entropy, which can coalesce primal confidence score maps and create an optimal confidence score map for more accurate localization. The target is localized on the peak of the optimal confidence score map. Besides, we introduce a collaborative optimization strategy to update circular and structural operators by iteratively training structural correlation filters, which significantly reduces computational complexity and improves robustness. Experimental results demonstrate that our approach achieves state-of-the-art performance in mean AUC scores of 71.5 and 69.4 on the OTB2013 and OTB2015 benchmarks respectively, and obtains a third-best expected average overlap (EAO) score of 29.8 on the VOT2017 benchmark.