On Probability Distributions for Trees: Representations, Inference and Learning

We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied class of tree series is the class of rational (or recognizable) tree series which can be defined either in an algebraic way or by means of multiplicity tree automata. We argue that the algebraic representation is very convenient to model probability distributions over a free algebra of trees. First, as in the string case, the algebraic representation allows to design learning algorithms for the whole class of probability distributions defined by rational tree series. Note that learning algorithms for rational tree series correspond to learning algorithms for weighted tree automata where both the structure and the weights are learned. Second, the algebraic representation can be easily extended to deal with unranked trees (like XML trees where a symbol may have an unbounded number of children). Both properties are particularly relevant for applications: nondeterministic automata are required for the inference problem to be relevant (recall that Hidden Markov Models are equivalent to nondeterministic string automata); nowadays applications for Web Information Extraction, Web Services and document processing consider unranked trees

Hypernode Graphs for Learning from Binary Relations between Groups in Networks

International audienceThe aim of this paper is to propose methods for learning from interactions between groups in networks. We introduced hypernode graphs in Ricatte et al (2014) a formal model able to represent group interactions and able to infer individual properties as well. Spectral graph learning algorithms were extended to the case of hypern-ode graphs. As a proof-of-concept, we have shown how to model multiple players games with hypernode graphs and that spectral learning algorithms over hyper-node graphs obtain competitive results with skill ratings specialized algorithms. In this paper, we explore theoretical issues for hypernode graphs. We show that hypernode graph kernels strictly generalize over graph kernels and hypergraph kernels. We show that hypernode graphs correspond to signed graphs such that the matrix D − W is positive semidefinite. It should be noted that homophilic relations between groups may lead to non homophilic relations between individ-uals. Moreover, we also present some issues concerning random walks and the resistance distance for hypernode graphs

Learning from Positive and Unlabeled Examples

International audienceIn many machine learning settings, labeled examples are difficult to collect while unlabeled data are abundant. Also, for some binary classification problems, positive examples, that is examples of the target class, are available. Can these additional data be used to improve accuracy of supervised learning algorithms? We investigate in this paper the design of learning algorithms from positive and unlabeled data only. Many machine learning and data mining algorithms, such as decision tree induction algorithms and naive Bayes algorithms, only use examples in order to evaluate statistical queries (SQ-like algorithms). Kearns designed the Statistical Query learning model in order to describe these algorithms. Here, we design an algorithm scheme which transforms any SQ-like algorithm into an algorithm based on positive statistical queries (estimates for probabilities over the set of positive instances) and instance statistical queries (estimates for probabilities over the instance space). We prove that any class learnable in the Statistical Query learning model is learnable from positive statistical queries and instance statistical queries only if a lower bound on the weight of any target concept $f$ can be estimated in polynomial time. Then, we design a decision tree induction algorithm POSC4.5, based on C4.5, that uses only positive and unlabeled examples and we give experimental results for this algorithm. The case of imbalanced classes in the sense that one of the two classes (say the positive class) is heavily underrepresented compared to the other class remains open. This problem is challenging because it is encountered in many real-world applications

Series, Weighted Automata, Probabilistic Automata and Probability Distributions for Unranked Trees.

We study tree series and weighted tree automata over unranked trees. The message is that recognizable tree series for unranked trees can be defined and studied from recognizable tree series for binary representations of unranked trees. For this we prove results of Denis et al (2007) as follows. We extend hedge automata -- a class of tree automata for unranked trees -- to weighted hedge automata. We define weighted stepwise automata as weighted tree automata for binary representations of unranked trees. We show that recognizable tree series can be equivalently defined by weighted hedge automata or weighted stepwise automata. Then we consider real-valued tree series and weighted tree automata over the field of real numbers. We show that the result also holds for probabilistic automata -- weighted automata with normalisation conditions for rules. We also define convergent tree series and show that convergence properties for recognizable tree series are preserved via binary encoding. From Etessami and Yannakakis (2009), we present decidability results on probabilistic tree automata and algorithms for computing sums of convergent series. Last we show that streaming algorithms for unranked trees can be seen as slight transformations of algorithms on the binary representations

Hypernode Graphs for Spectral Learning on Binary Relations over Sets

Paper accepted for publication at ECML/PKDD 2014International audienceWe introduce hypernode graphs as weighted binary relations between sets of nodes: a hypernode is a set of nodes, a hyperedge is a pair of hypernodes, and each node in a hypernode of a hyperedge is given a non negative weight that represents the node contribution to the relation. Hypernode graphs model binary relations between sets of individuals while allowing to reason at the level of individuals. We present a spectral theory for hypernode graphs that allows us to introduce an unnormalized Laplacian and a smoothness semi-norm. In this framework, we are able to extend spectral graph learning algorithms to the case of hypernode graphs. We show that hypernode graphs are a proper extension of graphs from the expressive power point of view and from the spectral analysis point of view. Therefore hypernode graphs allow to model higher order relations whereas it is not true for hypergraphs as shown in~\cite{Agarwal2006}. In order to prove the potential of the model, we represent multiple players games with hypernode graphs and introduce a novel method to infer skill ratings from game outcomes. We show that spectral learning algorithms over hypernode graphs obtain competitive results with skill ratings specialized algorithms such as Elo duelling and TrueSkill

Learning n-ary Node Selecting Tree Transducers from Completely Annotated Examples

International audienceWe present the first algorithm for learning n-ary node selection queries in trees from completely annotated examples by methods of grammatical inference. We propose to represent n-ary queries by deterministic n-ary node selecting tree transducers (NSTTs), that are known to capture the class of MSO-definable n-ary queries. Despite of this highly expressive, we show that n-aryy queries, selecting a polynomially bounded number of tuples per tree, represented by deterministic NSTTs can be learned from polynomial time and data while allowing for efficient enumeration of query answers. An application to wrapper induction in Web information extraction yields encouraging results

A Spectral Framework for a Class of Undirected Hypergraphs

We extend the graph spectral framework to a new class of undirected hypergraphs with bipartite hyperedges. A bipartite hyperedge is a pair of disjoint sets of nodes in which every node is associated with a weight. A bipartite hyperedge can be viewed as a relation between two teams of nodes in which every node has a weighted contribution to its team. Undirected hypergraphs generalize over undirected graphs. Consistently with the case of graphs, we define the notions of hypergraph gradient, hypergraph Laplacian, and hypergraph kernel as the Moore-Penrose pseudoinverse of a hypergraph Laplacian. Therefore, smooth labeling of (teams of) nodes and hypergraph regularization methods can be performed. Contrary to the graph case, we show that the class of hypergraph Laplacians is closed by the pseudoinverse operation (thus it is also the class of hypergraphs kernels), and is closed by convex linear combination. Closure properties allow us to define (hyper)graph combinations and operations while keeping a hypergraph interpretation of the result. We exhibit a subclass of signed graphs that can be associated with hypergraphs in a constructive way. A hypergraph and its associated signed graph have the same Laplacian. This property allows us to define a distance between nodes in undirected hypergraphs as well as in the subclass of signed graphs. The distance coincides with the usual definition of commute-time distance when the equivalent signed graph turns out to be a graph. We claim that undirected hypergraphs open the way to solve new learning tasks and model new problems based on set similarity or dominance. We are currently exploring applications for modeling games between teams and for graph summarization

Efficient Inclusion Checking for Deterministic Tree Automata and DTDs

International audienceWe present a new algorithm for testing language inclusion L(A) ⊆ L(B)L(A) between tree automata in time O(|A| |B|) where B is deterministic. We extend this algorithm for testing inclusion between automata for unranked trees A and deterministic DTDs D in time O(|A| |Σ| |D|). No previous algorithms with these complexities exist. A journal extension is available at http://hal.inria.fr/inria-00366082

Interactive Tuples Extraction from Semi-Structured Data

International audienceThis paper studies from a machine learning viewpoint the problem of extracting tuples of a target n-ary relation from tree structured data like XML or XHTML documents. Our system can extract, without any post-processing, tuples for all data structures including nested, rotated and cross tables. The wrapper induction algorithm we propose is based on two main ideas. It is incremental: partial tuples are extracted by increasing length. It is based on a representation-enrichment procedure: partial tuples of length i are encoded with the knowledge of extracted tu- ples of length i − 1. The algorithm is then set in a friendly interactive wrapper induction system for Web documents. We evaluate our system on several information extraction tasks over corporate Web sites. It achieves state-of-the-art results on simple data structures and succeeds on complex data structures where previous approaches fail. Experiments also show that our interactive framework significantly reduces the number of user interactions needed to build a wrapper

Exploring Category Structure with Contextual Language Models and Lexical Semantic Networks

Recent work on predicting category structure with distributional models, using either static word embeddings (Heyman and Heyman, 2019) or contextualized language models (CLMs) (Misra et al., 2021), report low correlations with human ratings, thus calling into question their plausibility as models of human semantic memory. In this work, we revisit this question testing a wider array of methods for probing CLMs for predicting typicality scores. Our experiments, using BERT (Devlin et al., 2018), show the importance of using the right type of CLM probes, as our best BERT-based typicality prediction methods substantially improve over previous works. Second, our results highlight the importance of polysemy in this task: our best results are obtained when using a disambiguation mechanism. Finally, additional experiments reveal that Information Contentbased WordNet (Miller, 1995), also endowed with disambiguation, match the performance of the best BERT-based method, and in fact capture complementary information, which can be combined with BERT to achieve enhanced typicality predictions