Abstract Machine learning from graphs is an established branch of AI research motivated by the relevance of applications that involve graph-structured data. The most popular instance is the graph neural network (GNN). On the other hand, due to the promising results of deep learning models in the most diverse fields of application, several efforts have been made to replicate these successes when dealing with graphical data. A prominent specimen of the kind is the graph convolutional network (GCN). Along these lines, the paper propose a novel approach for processing graphs that exploits the capabilities of convolutional neural networks (CNNs) to learn from images. This is achieved by means of a new representation of graphs, called GrapHisto, that portrays graphs in the form of characteristic “pictures”. The GrapHisto is in the form of graph-specific, unique tensors encapsulating the graph topology and its features (i.e., the labels associated with vertexes and edges). This representation is fed to a CNN, and the resulting machine is termed GrapHisto-CNN. The paper provides some theoretical investigations of the properties of the approach, and proposes solutions to some practical issues. An experimental evaluation of the GrapHisto-CNN is reported, revolving around two setups: classification of synthetically-generated graphs, and molecule classification form the dataset QM9. The results show that the approach is effective and robust, and that it compares favorably with GNNs and GCNs.

Abstract Albeit worryingly underrated in the recent literature on machine learning in general (and, on deep learning in particular), multivariate density estimation is a fundamental task in many applications, at least implicitly, and still an open issue. With a few exceptions, deep neural networks (DNNs) have seldom been applied to density estimation, mostly due to the unsupervised nature of the estimation task, and (especially) due to the need for constrained training algorithms that ended up realizing proper probabilistic models that satisfy Kolmogorov’s axioms. Moreover, in spite of the well-known improvement in terms of modeling capabilities yielded by mixture models over plain single-density statistical estimators, no proper mixtures of multivariate DNN-based component densities have been investigated so far. The paper fills this gap by extending our previous work on neural mixture densities (NMMs) to multivariate DNN mixtures. A maximum-likelihood (ML) algorithm for estimating Deep NMMs (DNMMs) is handed out, which satisfies numerically a combination of hard and soft constraints aimed at ensuring satisfaction of Kolmogorov’s axioms. The class of probability density functions that can be modeled to any degree of precision via DNMMs is formally defined. A procedure for the automatic selection of the DNMM architecture, as well as of the hyperparameters for its ML training algorithm, is presented (exploiting the probabilistic nature of the DNMM). Experimental results on univariate and multivariate data are reported on, corroborating the effectiveness of the approach and its superiority to the most popular statistical estimation techniques.

The paper copes with the task of automatic assessment of second language proficiency from the language learners' spoken responses to test prompts. The task has significant relevance to the field of computer assisted language learning. The approach presented in the paper relies on two separate modules: (1) an automatic speech recognition system that yields text transcripts of the spoken interactions involved, and (2) a multiple classifier system based on deep learners that ranks the transcripts into proficiency classes. Different deep neural network architectures (both feed-forward and recurrent) are specialized over diverse representations of the texts in terms of: a reference grammar, the outcome of probabilistic language models, several word embeddings, and two bag-of-word models. Combination of the individual classifiers is realized either via a probabilistic pseudo-joint model, or via a neural mixture of experts. Using the data of the third Spoken CALL Shared Task challenge, the highest values to date were obtained in terms of three popular evaluation metrics.

Structured data in the form of labeled graphs (with variable order and topology) may be thought of as the outcomes of a random graph (RG) generating process characterized by an underlying probabilistic law. This paper formalizes the notions of generalized RG (GRG) and probability density function (pdf) for GRGs. Thence, a "universal" learning machine (combining the encoding module of a recursive neural network and a radial basis functions' network) is introduced for estimating the unknown pdf from an unsupervised sample of GRGs. A maximum likelihood training algorithm is presented and constrained so as to ensure that the resulting model satisfies the axioms of probability. Techniques for preventing the model from degenerate solutions are proposed, as well as variants of the algorithm suitable to the tasks of graphs classification and graphs clustering. The major properties of the machine are discussed. The approach is validated empirically through experimental investigations in the estimation of pdfs for synthetic and real-life GRGs, in the classification of images from the Caltech Benchmark data set and molecules from the Mutagenesis data set, and in clustering of images from the LabelMe data set.

Human action recognition in video streams is a fast developing field in pattern recognition and machine learning. Local image representations, e.g. space-time interest points [1], have proven to be the current most reliable choice of feature in sequences in which the region of interest is difficult to determine [2]. However, the question how to deal with more severe occlusions has large been ignored [2]. This work proposes a new approach which directly addresses heavy occlusions by modeling the skeleton-based features using a probability density functions (PDF) defined over graphs. We integrated the proposed density into an hidden Markov model (HMM) to model sequences of graphs of arbitrary sizes, i.e. occlusions setting may change over time. The approach is evaluated using a dataset embracing three action classes, studying six different types of occlusions (involving the removal of subgraphs from the graphical representation of action sequence). The presented study shows clearly that actions from even heavily occluded sequences can be reliably recognized.

Hybrid random fields are a recently proposed graphical model for pseudo-likelihood estimation in discrete domains. In this paper, we develop a continuous version of the model for nonparametric density estimation. To this aim, Nadaraya-Watson kernel estimators are used to model the local conditional densities within hybrid random fields. First, we introduce a heuristic algorithm for tuning the kernel bandwidhts in the conditional density estimators. Second, we propose a novel method for initializing the structure learning algorithm originally employed for hybrid random fields, which was meant instead for discrete variables. In order to test the accuracy of the proposed technique, we use a number of synthetic pattern classification benchmarks, generated from random distributions featuring nonlinear correlations between the variables. As compared to state-of-the-art nonparametric and semiparametric learning techniques for probabilistic graphical models, kernel-based hybrid random fields regularly outperform each considered alternative in terms of recognition accuracy, while preserving the scalability properties (with respect to the number of variables) that originally motivated their introduction.

In this paper we propose a hybrid probabilistic graphical model for pseudo-likelihood estimation in high-dimensional domains. The model is based on Bayesian networks and Markov random fields. On the one hand, we prove that the proposed model is more expressive than Bayesian networks in terms of the representable distributions. On the other hand, we develop a computationally efficient structure learning algorithm, and we provide theoretical and experimental evidence showing how the modular nature of our model allows structure learning to scale up very well to high-dimensional datasets. The capability of the hybrid model to accurately learn complex networks of conditional independencies is illustrated by promising results in pattern recognition applications.

One major problem in pattern recognition is estimating probability density functions. Unfortunately, parametric techniques rely on an arbitrary assumption on the form of the underlying, unknown density function. On the other hand, nonparametric techniques, such as the popular kn-nearest neighbor (not to be confused with the k-nearest neighbor classification algorithm), allow to remove such an assumption. Albeit effective, the kn-nearest neighbor is affected by a number of limitations. Artificial neural networks are, in principle, an alternative family of nonparametric models. So far, artificial neural networks have been extensively used to estimate probabilities (e.g., class-posterior probabilities). However, they have not been exploited to estimate instead probability density functions. This paper introduces a simple, neural-based algorithm for unsupervised, nonparametric estimation of multivariate densities, relying on the kn-nearest neighbor technique. This approach overcomes the limitations of kn-nearest neighbor, possibly improving the estimation accuracy of the resulting pdf models. An experimental investigation of the algorithm behavior is offered, exploiting random samples drawn from a mixture of Fisher-Tippett density functions.

Learning probabilistic graphical models from high-dimensional datasets is a computationally challenging task. In many interesting applications, the domain dimensionality is such as to prevent state-of-the-art statistical learning techniques from delivering accurate models in reasonable time. This paper presents a hybrid random field model for pseudo-likelihood estimation in high-dimensional domains. A theoretical analysis proves that the class of pseudo-likelihood distributions representable by hybrid random fields strictly includes the class of joint probability distributions representable by Bayesian networks. In order to learn hybrid random fields from data, we develop the Markov Blanket Merging algorithm. Theoretical and experimental evidence shows that Markov Blanket Merging scales up very well to high-dimensional datasets. As compared to other widely used statistical learning techniques, Markov Blanket Merging delivers accurate results in a number of link prediction tasks, while achieving also significant improvements in terms of computational efficiency.

Several problems in bioinformatics and cheminformatics concern the classification of molecules. Relevant instances are automatic cancer detection/classification, machine-learning pathologic prediction, automatic predictive toxicology, etc. Molecules may be represented in terms of graphical structures in a natural way: each node in the graph can be used to represent an atom, whilst the edges of the graph represent the atom-atom bonds. Labels (in the form of real-valued vectors) are associated with nodes and edges in order to express physical and chemical properties of the corresponding atoms and bonds, respectively. These structured data are expected to contain more information than a traditional (flat) feature vector, information that may strengthen the classification capabilities of a machine learner. This paper investigates the application of a novel Bayesian/connectionist classifier to this graphical pattern recognition task. The approach is much simpler than state-of-the-art machine learning paradigms for graphical/relational learning. It relies on the idea of describing the graph in terms of a binary relation. The posterior probability of a class given the relation is estimated as a function of probabilistic quantities modeled with a neural network, trained over individual vertex pairs in the graph. The popular and challenging Mutagenesis dataset is considered for the experimental evaluation. Despite its simplicity, the technique turns out to yield the highest recognition accuracies to date on the complete (friendly + unfriendly) dataset, outperforming complex machines (relational and graph neural nets, kernels for graphs, inductive logic programming techniques, etc.). Some preliminary chemical/biological implications are eventually hypothesized in the light of the results obtained.

Spoken human-machine interaction in real-world environments requires acoustic models that are robust to changes in acoustic conditions, e.g. presence of noise. Unfortunately, the popular hidden Markov models (HMM) are not noise tolerant. One way to increase recognition performance rely on the acquisition of a small adaptation set of noisy utterances, that is used to estimate a normalization mapping between noisy and clean features to be fed into the acoustic model. In this research we develop a maximum-likelihood gradient-ascent training algorithm (instead of the usual least squares regression) for a neural normalization module to be combined with a hybrid connectionist/HMM recognizer. The algorithm is inspired by the so-called "inversion principle". Simulation results on a real-world speaker-independent continuous speech corpus of connected Italian digits, corrupted by additive noise, validate the approach: a small neural net (13 hidden neurons) trained over a single adaptation utterance for just one iteration yields 18.79% relative word error rate (WER) reduction over the bare hybrid, and a 65.10% relative WER reduction over the Gaussian-based HMM

Monitoring the values of physical variables in water at ground level (in a river, lake or ocean) on the basis of noisy images acquired from a geostationary satellite is a relevant and challenging task. This paper introduces a 3-module neural system that allows for automatic monitoring of the local concentration of chlorophyll in presence of clouds and turbid water at specific locations. The system relies on images in four different wavelength intervals taken by the satellite over specific points of the lake surface. Module (1) estimates the probability of presence of clouds over dots in the image, possibly applying the reject option, and feeding this information into the following nets. Module (2) estimates the turbidity of water, i.e., its transparency, on a dot-by-dot basis. Finally, module (3) is a neural network with adaptive amplitude of activation functions, featuring a combination of linear and nonlinear terms, that realizes a regression model to describe the relationship between its inputs (i.e., a 4-bands dot in the satellite image plus the corresponding outputs from the previous two modules) and the desired concentration of chlorophyll in the corresponding location of the lake. Eventually, a global tuning of the whole system parameters is possible. Experiments involving noisy data, sampled from the water of Lake Montepulciano in Tuscany (Italy), are presented. The problem of the limited availability of "target" training data, i.e. physical measurements obtained by sampling from the lake surface on boats, is addressed. Results are compared with standard multivariate linear regression models.

The Aurora 2 database may be used as a benchmark for evaluation of algorithms under noisy conditions. In particular, the clean training/noisy test mode is aimed at evaluating models that are trained on clean data only without further adjustments on the noisy data, i.e. under severe mismatch between the training and test conditions. While several researchers proposed techniques at the front-end level to improve recognition performance over the reference hideen Markov model (HMM) baseline, investigations at the back-end level are sought. In this respect, the goal is to develop acoustic models that are intrinsically less noise sensitive. This paper presents the word accuracy yielded by a non-parametric HMM with connectionist estimates of the emission probabilities, i.e. a neural network is applied instead of the usual parametric (Gaussian mixture) probability densities. A regularization technique, relying on a maximum-likelihood parameter grouping algorithm, is explicitly introduced to increase the generalization capability of the model and, in turn, its noise-robustness. Results show that a 15,43% relative word error rate reduction w.r.t. the Gaussianmixture HMM is obtained by averaging over the different noises and SNRs of Aurora 2 test set A.

Acoustic modeling in state-of-the-art speech recognition systems usually relies on hidden Markov models (HMMs) with Gaussian emission densities. HMMs suffer from intrinsic limitations, mainly due to their arbitrary parametric assumption. Artificial neural networks (ANNs) appear to be a promising alternative in this respect, but they historically failed as a general solution to the acoustic modeling problem. This paper introduces algorithms based on a gradient-ascent technique for global training of a hybrid ANN/HMM system, in which the ANN is trained for estimating the emission probabilities of the states of the HMM. The approach is related to the major hybrid systems proposed by Bourlard and Morgan and by Bengio, with the aim of combining their benefits within a unified framework and to overcome their limitations. Several viable solutions to the "divergence problem"-that may arise when training is accomplished over the maximum-likelihood (ML) criterion-are proposed. Experimental results in speaker-independent, continuous speech recognition over Italian digit-strings validate the novel hybrid framework, allowing for improved recognition performance over HMMs with mixtures of Gaussian components, as well as over Bourlard and Morgan's paradigm. In particular, it is shown that the maximum a posteriori (MAP) version of the algorithm yields a 46.34% relative word error rate reduction with respect to standard HMMs.

The segmental neural network (SNN) architecture was introduced at BBN by Zavaliagkos et al. (1994) for rescoring the N-best hypothesis yielded by a standard continuous density hidden Markov model (CDHMM) applied to automatic speech recognition. An enhanced connectionist model, called SNN with trainable amplitude of activation functions (SNN-TA), presented for use instead of the CDHMM to perform the recognition of isolated words. Viterbi-based segmentation is then introduced, relying on the level building algorithm, that can be combined with the SNN-TA to obtain a hybrid framework for continuous speech recognition. The present paradigm is applied to the recognition of isolated digits, collected in a real car environment under several noisy conditions (traffic, speed, road conditions, etc.) using a microphone placed far from the talker. We stress the fact that robustness to noise can be increased by improving the generalization capabilities of the speech recognizer. In this perspective, while CDHMM completely lack of a proper regularization theory, a regularized SNN-TA model is discussed, which yields effective generalization and noise-tolerance, outperforming the CDHMM on the noisy task under consideration.

Network training algorithms have heavily concentrated on the learning of connection weights. Little effort has been made to learn the amplitude of the activation functions, which defines the range of values that the function can take. This paper introduces novel algorithms to learn the amplitudes of nonlinear activations in layered networks, without any assumption on their analytical form. Three instances of the algorithms are developed: (i) a common amplitude is shared among all the nonlinear units; (ii) each layer has its own amplitude; (iii) neuron-specific amplitudes are allowed. Experimental results validate the approach to a large extent, showing a dramatic improvement in performance over the nets with fixed amplitudes.

This paper introduces a hybrid system for modeling, learning and recognition of sequences of 'states' in indoor robot navigation. States are broadly defined as local relevant situations (in the real world) in which the robot happens to be during the navigation. The hybrid is based on parallel recurrent neural networks trained to perform a posteriori state probability estimates of an underlying hidden Markov model (HMM) given a sequence of sensory (e.g. sonar) observations. Discriminative training is accomplished in a supervised manner, using gradient-descent. Recognition is carried out either in a dynamic programming framework, i.e. searching the maximum a posteriori probability of state-posteriors along paths of the HMM, or in real time. The approach is suitable for navigation and for map learning. Experiments of learning and recognition of noisy sequences acquired by a mobile robot equipped with 16 sonars are presented.

This paper introduces bootstrap error estimation for automatic tuning of parameters in combined networks, applied as front-end preprocessors for a speech recognition system based on hidden Markov models. The method is evaluated on a large-vocabulary (10 000 words) continuous speech recognition task. Bootstrap estimates of minimum mean squared error allow selection of speaker normalization models improving recognition performance. The procedure allows a flexible strategy for dealing with inter-speaker variability without requiring an additional validation set. Recognition results are compared for linear, generalized radial basis functions and multi-layer perceptron network architectures.

The paper presents a rapid speaker-normalization technique based on neural network spectral mapping. The neural network is used as a front-end of a continuous speech recognition system (speaker(cid:173) dependent, HMM-based) to normalize the input acoustic data from a new speaker. The spectral difference between speakers can be reduced using a limited amount of new acoustic data (40 phonet(cid:173) ically rich sentences). Recognition error of phone units from the acoustic-phonetic continuous speech corpus APASCI is decreased with an adaptability ratio of 25%. We used local basis networks of elliptical Gaussian kernels, with recursive allocation of units and on-line optimization of parameters (GRAN model). For this ap(cid:173) plication, the model included a linear term. The results compare favorably with multivariate linear mapping based on constrained orthonormal transformations.