[Abridged] Although galaxies are found to follow a tight relation between their star formation rate and stellar mass, they are expected to exhibit complex star formation histories (SFH), with short-term fluctuations. The goal of this pilot study is to present a method that will identify galaxies that are undergoing a strong variation of star formation activity in the last tens to hundreds Myr. In other words, the proposed method will determine whether a variation in the last few hundreds of Myr of the SFH is needed to properly model the SED rather than a smooth normal SFH. To do so, we analyze a sample of COSMOS galaxies using high signal-to-noise ratio broad band photometry. We apply Approximate Bayesian Computation, a state-of-the-art statistical method to perform model choice, associated to machine learning algorithms to provide the probability that a flexible SFH is preferred based on the observed flux density ratios of galaxies. We present the method and test it on a sample of simulated SEDs. The input information fed to the algorithm is a set of broadband UV to NIR (rest-frame) flux ratios for each galaxy. The method has an error rate of 21% in recovering the right SFH and is sensitive to SFR variations larger than 1 dex. A more traditional SED fitting method using CIGALE is tested to achieve the same goal, based on fits comparisons through Bayesian Information Criterion but the best error rate obtained is higher, 28%. We apply our new method to the COSMOS galaxies sample. The stellar mass distribution of galaxies with a strong to decisive evidence against the smooth delayed-$\tau$ SFH peaks at lower M* compared to galaxies where the smooth delayed-$\tau$ SFH is preferred. We discuss the fact that this result does not come from any bias due to our training. Finally, we argue that flexible SFHs are needed to be able to cover that largest SFR-M* parameter space possible.

A fundamental question in modern machine learning is how deep neural networks can generalize. We address this question using 1) an equivalence between training infinitely wide neural networks and performing kernel regression with a deterministic kernel called the Neural Tangent Kernel (NTK) (Jacot et al. 2018), and 2) theoretical tools from statistical physics. We derive analytical expressions for learning curves for kernel regression, and use them to evaluate how the test loss of a trained neural network depends on the number of samples. Our approach allows us not only to compute the total test risk but also the decomposition of the risk due to different spectral components of the kernel. Complementary to recent results showing that during gradient descent, neural networks fit low frequency components first, we identify a new type of frequency principle: as the size of the training set size grows, kernel machines and neural networks begin to fit successively higher frequency modes of the target function. We verify our theory with simulations of kernel regression and training wide artificial neural networks.

Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However this sparsity tends not to be homogeneous, and networks can also be locally dense, for example with a few nodes connecting to a large fraction of the rest of the network, or with small groups of nodes with a large probability of connections between them. Here we show how latent Poisson models which generate hidden multigraphs can be effective at capturing this density heterogeneity, while being more tractable mathematically than some of the alternatives that model simple graphs directly. We show how these latent multigraphs can be reconstructed from data on simple graphs, and how this allows us to disentangle dissortative degree-degree correlations from the constraints of imposed degree sequences, and to improve the identification of community structure in empirically relevant scenarios.

Outlier, or anomaly, detection is essential for optimal performance of machine learning methods and statistical predictive models. It is not just a technical step in a data cleaning process but a key topic in many fields such as fraudulent document detection, in medical applications and assisted diagnosis systems or detecting security threats. In contrast to population-based methods, neighborhood based local approaches are simple flexible methods that have the potential to perform well in small sample size unbalanced problems. However, a main concern of local approaches is the impact that the computation of each sample neighborhood has on the method performance. Most approaches use a distance in the feature space to define a single neighborhood that requires careful selection of several parameters. This work presents a local approach based on a local measure of the heterogeneity of sample labels in the feature space considered as a topological manifold. Topology is computed using the communities of a weighted graph codifying mutual nearest neighbors in the feature space. This way, we provide with a set of multiple neighborhoods able to describe the structure of complex spaces without parameter fine tuning. The extensive experiments on real-world data sets show that our approach overall outperforms, both, local and global strategies in multi and single view settings.

Neural networks and tree ensembles are state-of-the-art learners, each with its unique statistical and computational advantages. We aim to combine these advantages by introducing a new layer for neural networks, composed of an ensemble of differentiable decision trees (a.k.a. soft trees). While differentiable trees demonstrate promising results in the literature, in practice they are typically slow in training and inference as they do not support conditional computation. We mitigate this issue by introducing a new sparse activation function for sample routing, and implement true conditional computation by developing specialized forward and backward propagation algorithms that exploit sparsity. Our efficient algorithms pave the way for jointly training over deep and wide tree ensembles using first-order methods (e.g., SGD). Experiments on 23 classification datasets indicate over 10x speed-ups compared to the differentiable trees used in the literature and over 20x reduction in the number of parameters compared to gradient boosted trees, while maintaining competitive performance. Moreover, experiments on CIFAR, MNIST, and Fashion MNIST indicate that replacing dense layers in CNNs with our tree layer reduces the test loss by 7-53% and the number of parameters by 8x. We provide an open-source TensorFlow implementation with a Keras API.

An important problem in multiview representation learning is finding the optimal combination of views with respect to the specific task at hand. To this end, we introduce NAM: a Neural Attentive Multiview machine that learns multiview item representations and similarity by employing a novel attention mechanism. NAM harnesses multiple information sources and automatically quantifies their relevancy with respect to a supervised task. Finally, a very practical advantage of NAM is its robustness to the case of dataset with missing views. We demonstrate the effectiveness of NAM for the task of movies and app recommendations. Our evaluations indicate that NAM outperforms single view models as well as alternative multiview methods on item recommendations tasks, including cold-start scenarios.

We introduce the use of autoregressive normalizing flows for rapid likelihood-free inference of binary black hole system parameters from gravitational-wave data with deep neural networks. A normalizing flow is an invertible mapping on a sample space that can be used to induce a transformation from a simple probability distribution to a more complex one: if the simple distribution can be rapidly sampled and its density evaluated, then so can the complex distribution. Our first application to gravitational waves uses an autoregressive flow, conditioned on detector strain data, to map a multivariate standard normal distribution into the posterior distribution over system parameters. We train the model on artificial strain data consisting of IMRPhenomPv2 waveforms drawn from a five-parameter $(m_1, m_2, \phi_0, t_c, d_L)$ prior and stationary Gaussian noise realizations with a fixed power spectral density. This gives performance comparable to current best deep-learning approaches to gravitational-wave parameter estimation. We then build a more powerful latent variable model by incorporating autoregressive flows within the variational autoencoder framework. This model has performance comparable to Markov chain Monte Carlo and, in particular, successfully models the multimodal $\phi_0$ posterior. Finally, we train the autoregressive latent variable model on an expanded parameter space, including also aligned spins $(\chi_{1z}, \chi_{2z})$ and binary inclination $\theta_{JN}$, and show that all parameters and degeneracies are well-recovered. In all cases, sampling is extremely fast, requiring less than two seconds to draw $10^4$ posterior samples.

We present a method for financial time series forecasting using representation learning techniques. Recent progress on deep autoregressive models has shown their ability to capture long-term dependencies of the sequence data. However, the shortage of available financial data for training will make the deep models susceptible to the overfitting problem. In this paper, we propose a neural-network-powered conditional mutual information (CMI) estimator for learning representations for the forecasting task. Specifically, we first train an encoder to maximize the mutual information between the latent variables and the label information conditioned on the encoded observed variables. Then the features extracted from the trained encoder are used to learn a subsequent logistic regression model for predicting time series movements. Our proposed estimator transforms the CMI maximization problem to a classification problem whether two encoded representations are sampled from the same class or not. This is equivalent to perform pairwise comparisons of the training datapoints, and thus, improves the generalization ability of the deep autoregressive model. Empirical experiments indicate that our proposed method has the potential to advance the state-of-the-art performance.

Graph neural networks (GNNs) have received much attention recently because of their excellent performance on graph-based tasks. However, existing research on GNNs focuses on designing more effective models without considering much the quality of the input data itself. In this paper, we propose self-enhanced GNN, which improves the quality of the input data using the outputs of existing GNN models for better performance on semi-supervised node classification. As graph data consist of both topology and node labels, we improve input data quality from both perspectives. For topology, we observe that higher classification accuracy can be achieved when the ratio of inter-class edges (connecting nodes from different classes) is low and propose topology update to remove inter-class edges and add intra-class edges. For node labels, we propose training node augmentation, which enlarges the training set using the labels predicted by existing GNN models. As self-enhanced GNN improves the quality of the input graph data, it is general and can be easily combined with existing GNN models. Experimental results on three well-known GNN models and seven popular datasets show that self-enhanced GNN consistently improves the performance of the three models. The reduction in classification error is 16.2% on average and can be as high as 35.1%.

Land-use regression (LUR) models are important for the assessment of air pollution concentrations in areas without measurement stations. While many such models exist, they often use manually constructed features based on restricted, locally available data. Thus, they are typically hard to reproduce and challenging to adapt to areas beyond those they have been developed for. In this paper, we advocate a paradigm shift for LUR models: We propose the Data-driven, Open, Global (DOG) paradigm that entails models based on purely data-driven approaches using only openly and globally available data. Progress within this paradigm will alleviate the need for experts to adapt models to the local characteristics of the available data sources and thus facilitate the generalizability of air pollution models to new areas on a global scale. In order to illustrate the feasibility of the DOG paradigm for LUR, we introduce a deep learning model called MapLUR. It is based on a convolutional neural network architecture and is trained exclusively on globally and openly available map data without requiring manual feature engineering. We compare our model to state-of-the-art baselines like linear regression, random forests and multi-layer perceptrons using a large data set of modeled $\text{NO}_2$ concentrations in Central London. Our results show that MapLUR significantly outperforms these approaches even though they are provided with manually tailored features. Furthermore, we illustrate that the automatic feature extraction inherent to models based on the DOG paradigm can learn features that are readily interpretable and closely resemble those commonly used in traditional LUR approaches.