An effective aggregation of node features into a graph-level representation via readout functions is an essential step in numerous learning tasks involving graph neural networks. Typically, readouts are simple and non-adaptive functions designed such that the resulting hypothesis space is permutation invariant. Prior work on deep sets indicates that such readouts might require complex node embeddings that can be difficult to learn via standard neighborhood aggregation schemes. Motivated by this, we investigate the potential of adaptive readouts given by neural networks that do not necessarily give rise to permutation invariant hypothesis spaces. We argue that in some problems such as binding affinity prediction where molecules are typically presented in a canonical form it might be possible to relax the constraints on permutation invariance of the hypothesis space and learn a more effective model of the affinity by employing an adaptive readout function. Our empirical results demonstrate the effectiveness of neural readouts on more than 40 datasets spanning different domains and graph characteristics. Moreover, we observe a consistent improvement over standard readouts (i.e., sum, max, and mean) relative to the number of neighborhood aggregation iterations and different convolutional operators.

We study the problem of learning robust acoustic models in adverse environments, characterized by a significant mismatch between training and test conditions. This problem is of paramount importance for the deployment of speech recognition systems that need to perform well in unseen environments. First, we characterize data augmentation theoretically as an instance of vicinal risk minimization, which aims at improving risk estimates during training by replacing the delta functions that define the empirical density over the input space with an approximation of the marginal population density in the vicinity of the training samples. More specifically, we assume that local neighborhoods centered at training samples can be approximated using a mixture of Gaussians, and demonstrate theoretically that this can incorporate robust inductive bias into the learning process. We then specify the individual mixture components implicitly via data augmentation schemes, designed to address common sources of spurious correlations in acoustic models. To avoid potential confounding effects on robustness due to information loss, which has been associated with standard feature extraction techniques (e.g., fbank and mfcc features), we focus on the waveform-based setting. Our empirical results show that the approach can generalize to unseen noise conditions, with 150% relative improvement in out-of-distribution generalization compared to training using the standard risk minimization principle. Moreover, the results demonstrate competitive performance relative to models learned using a training sample designed to match the acoustic conditions characteristic of test utterances.

Due to limited computational resources, acoustic models of early automatic speech recognition ( ASR ) systems were built in low-dimensional feature spaces that incur considerable information loss at the outset of the process. Several comparative studies of automatic and human speech recognition suggest that this information loss can adversely affect the robustness of ASR systems. To mitigate that and allow for learning of robust models, we propose a deep 2 D convolutional network in the waveform domain. The first layer of the network decomposes waveforms into frequency sub-bands, thereby representing them in a structured high-dimensional space. This is achieved by means of a parametric convolutional block defined via cosine modulations of compactly supported windows. The next layer embeds the wave-form in an even higher-dimensional space of high-resolution spectro-temporal patterns, implemented via a 2 D convolutional block. This is followed by a gradual compression phase that selects most relevant spectro-temporal patterns using wide-pass 2 D filtering. Our results show that the approach significantly out-performs alternative waveform-based models on both noisy and spontaneous conversational speech ( 24% and 11% relative error reduction, respectively). Moreover, this study provides empirical evidence that learning directly from the waveform domain could be more effective than learning using hand-crafted features.

Deep scattering spectrum consists of a cascade of wavelet transforms and modulus non-linearity. It generates features of different orders, with the first order coefficients approximately equal to the Mel-frequency cepstrum, and higher order coefficients recovering information lost at lower levels. We investigate the effect of including the information recovered by higher order coefficients on the robustness of speech recognition. To that end, we also propose a modification to the original scattering transform tailored for noisy speech. In particular, instead of the modulus non-linearity we opt to work with power coefficients and, therefore, use the squared modulus non-linearity. We quantify the robustness of scattering features using the word error rates of acoustic models trained on clean speech and evaluated using sets of utterances corrupted with different noise types. Our empirical results show that the second order scattering power spectrum coefficients capture invariants relevant for noise robustness and that this additional information improves generalization to unseen noise conditions (almost 20% relative error reduction on AURORA 4). This finding can have important consequences on speech recognition systems that typically discard the second order information and keep only the first order features (known for emulating MFCC and FBANK values) when representing speech.

Due to limited computational resources, acoustic models of early automatic speech recognition ( ASR ) systems were built in low-dimensional feature spaces that incur considerable information loss at the outset of the process. Several comparative studies of automatic and human speech recognition suggest that this information loss can adversely affect the robustness of ASR systems. To mitigate that and allow for learning of robust models, we propose a deep 2 D convolutional network in the waveform domain. The first layer of the network decomposes waveforms into frequency sub-bands, thereby representing them in a structured high-dimensional space. This is achieved by means of a parametric convolutional block defined via cosine modulations of compactly supported windows. The next layer embeds the waveform in an even higher-dimensional space of high-resolution spectro-temporal patterns, implemented via a 2 D convolutional block. This is followed by a gradual compression phase that selects most relevant spectro-temporal patterns using wide-pass 2 D filtering. Our results show that the approach significantly outperforms alternative waveform-based models on both noisy and spontaneous conversational speech ( 24% and 11% relative error reduction, respectively). Moreover, this study provides empirical evidence that learning directly from the waveform domain could be more effective than learning using hand-crafted features. by means of a non-parametric 2 D convolutional layer. is followed

We propose a novel family of band-pass filters for efficient spectral decomposition of signals. Previous work has already established the effectiveness of representations based on static band-pass filtering of speech signals (e.g., mel-frequency cepstral coefficients and deep scattering spectrum). A potential shortcoming of these approaches is the fact that the parameters specifying such a representation are fixed a priori and not learned using the available data. To address this limitation, we propose a family of filters defined via cosine modulations of Parzen windows, where the modulation frequency models the center of a spectral band-pass filter and the length of a Parzen window is inversely proportional to its bandwidth. We propose to learn these filters as part of a multilayer convolutional operator using stochastic variational inference based on Gaussian dropout posteriors and sparsity inducing priors. Such a prior leads to an intractable integral defining the Kullback--Leibler divergence term for which we propose an effective approximation based on the Gauss--Hermite quadrature. Our empirical results demonstrate that modulation filter-learning can be statistically significantly more effective than static band-pass filtering on continuous speech recognition from raw speech. This is also the first work to achieve state-of-the-art results on speech recognition using variational inference.

We investigate the potential of stochastic neural networks for learning effective waveform-based acoustic models. The waveform-based setting, inherent to fully end-to-end speech recognition systems, is motivated by several comparative studies of automatic and human speech recognition that associate standard non-adaptive feature extraction techniques with information loss, which can adversely affect robustness. Stochastic neural networks, on the other hand, are a class of models capable of incorporating rich regularization mechanisms into the learning process. We consider a deep convolutional neural network that first decomposes speech into frequency sub-bands via an adaptive parametric convolutional block where filters are specified by cosine modulations of compactly supported windows. The network then employs standard non-parametric 1D convolutions to extract relevant spectro-temporal patterns while gradually compressing the structured high dimensional representation generated by the parametric block. We rely on a probabilistic parametrization of the proposed neural architecture and learn the model using stochastic variational inference. This requires evaluation of an analytically intractable integral defining the Kullback–Leibler divergence term responsible for regularization, for which we propose an effective approximation based on the Gauss–Hermite quadrature. Our empirical results demonstrate a superior performance of the proposed approach over comparable waveform-based baselines and indicate that it could lead to robustness. Moreover, the approach outperforms a recently proposed deep convolutional neural network for learning of robust acoustic models with standard FBANK features.

We propose a novel family of band-pass filters for efficient spectral decomposition of signals. Previous work has already established the effectiveness of representations based on static band-pass filtering of speech signals (e.g., mel-frequency cepstral coefficients and deep scattering spectrum). A potential shortcoming of these approaches is the fact that the parameters specifying such a representation are fixed a priori and not learned using the available data. To address this limitation, we propose a family of filters defined via cosine modulations of Parzen windows, where the modulation frequency models the center of a spectral band-pass filter and the length of a Parzen window is inversely proportional to the filter width in the spectral domain. We propose to learn such a representation using stochastic variational Bayesian inference based on Gaussian dropout posteriors and sparsity inducing priors. Such a prior leads to an intractable integral defining the Kullback--Leibler divergence term for which we propose an effective approximation based on the Gauss--Hermite quadrature. Our empirical results demonstrate that the proposed approach is competitive with state-of-the-art models on speech recognition tasks.

We provide the first mathematically complete derivation of the Nystr\"om method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building on this result, we devise highly scalable methods for learning in reproducing kernel Kre\u{\i}n spaces. The devised approaches provide a principled and theoretically well-founded means to tackle large scale learning problems with indefinite kernels. The main motivation for our work comes from problems with structured representations (e.g., graphs, strings, time-series), where it is relatively easy to devise a pairwise (dis)similarity function based on intuition and/or knowledge of domain experts. Such functions are typically not positive definite and it is often well beyond the expertise of practitioners to verify this condition. The effectiveness of the devised approaches is evaluated empirically using indefinite kernels defined on structured and vectorial data representations.

We extend the Nystr\"om method for low-rank approximation of positive definite Mercer kernels to approximation of indefinite kernel matrices. Our result is the first derivation of the approach that does not require the positive definiteness of the kernel function. Building on this result, we then devise highly scalable methods for learning in reproducing kernel Kre\u{\i}n spaces. The main motivation for our work comes from problems with structured representations (e.g., graphs, strings, time-series), where it is relatively easy to devise a pairwise (dis)similarity function based on intuition/knowledge of a domain expert. Such pairwise functions are typically not positive definite and it is often well beyond the expertise of practitioners to verify this condition. The proposed large scale approaches for learning in reproducing kernel Kre\u{\i}n spaces provide principled and theoretically well-founded means to tackle this class of problems. The effectiveness of the approaches is evaluated empirically using kernels defined on structured and vectorial data representations.

We formulate a novel regularized risk minimization problem for learning in reproducing kernel Krein spaces and show that the strong representer theorem applies to it. As a result of the latter, the learning problem can be expressed as the minimization of a quadratic form over a hypersphere of constant radius. We present an algorithm that can find a globally optimal solution to this nonconvex optimization problem in time cubic in the number of instances. Moreover, we derive the gradient of the solution with respect to its hyperparameters and, in this way, provide means for efficient hyperparameter tuning. The approach comes with a generalization bound expressed in terms of the Rademacher complexity of the corresponding hypothesis space. The major advantage over standard kernel methods is the ability to learn with various domain specific similarity measures for which positive definiteness does not hold or is difficult to establish. The approach is evaluated empirically using indefinite kernels defined on structured as well as vectorial data. The empirical results demonstrate a superior performance of our approach over the state-of-the-art baselines.

Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic bounds which are at odds with the empirical results. We tackle these problems and provide the first unified risk analysis of learning with random Fourier features using the squared error and Lipschitz continuous loss functions. In our bounds, the trade-off between the computational cost and the expected risk convergence rate is problem specific and expressed in terms of the regularization parameter and the \emph{number of effective degrees of freedom}. We study both the standard random Fourier features method for which we improve the existing bounds on the number of features required to guarantee the corresponding minimax risk convergence rate of kernel ridge regression, as well as a data-dependent modification which samples features proportional to \emph{ridge leverage scores} and further reduces the required number of features. As ridge leverage scores are expensive to compute, we devise a simple approximation scheme which provably reduces the computational cost without loss of statistical efficiency.

Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic bounds which are at odds with the empirical results. We tackle these problems and provide the first unified risk analysis of learning with random Fourier features using the squared error and Lipschitz continuous loss functions. In our bounds, the trade-off between the computational cost and the expected risk convergence rate is problem specific and expressed in terms of the regularization parameter and the \emph{number of effective degrees of freedom}. We study both the standard random Fourier features method for which we improve the existing bounds on the number of features required to guarantee the corresponding minimax risk convergence rate of kernel ridge regression, as well as a data-dependent modification which samples features proportional to \emph{ridge leverage scores} and further reduces the required number of features. As ridge leverage scores are expensive to compute, we devise a simple approximation scheme which provably reduces the computational cost without loss of statistical efficiency.

We consider lead discovery as active search in a space of labelled graphs. In particular, we extend our recent data‐driven adaptive Markov chain approach, and evaluate it on a focused drug design problem, where we search for an antagonist of an αv integrin, the target protein that belongs to a group of Arg−Gly−Asp integrin receptors. This group of integrin receptors is thought to play a key role in idiopathic pulmonary fibrosis, a chronic lung disease of significant pharmaceutical interest. As an in silico proxy of the binding affinity, we use a molecular docking score to an experimentally determined αvβ6 protein structure. The search is driven by a probabilistic surrogate of the activity of all molecules from that space. As the process evolves and the algorithm observes the activity scores of the previously designed molecules, the hypothesis of the activity is refined. The algorithm is guaranteed to converge in probability to the best hypothesis from an a priori specified hypothesis space. In our empirical evaluations, the approach achieves a large structural variety of designed molecular structures for which the docking score is better than the desired threshold. Some novel molecules, suggested to be active by the surrogate model, provoke a significant interest from the perspective of medicinal chemistry and warrant prioritization for synthesis. Moreover, the approach discovered 19 out of the 24 active compounds which are known to be active from previous biological assays.

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