The group affect or emotion in an image of people can be inferred by extracting features about both the people in the picture and the overall makeup of the scene. The state-of-the-art on this problem investigates a combination of facial features, scene extraction and even audio tonality. This paper combines three additional modalities, namely, human pose, text-based tagging and CNN extracted features / predictions. To the best of our knowledge, this is the first time all of the modalities were extracted using deep neural networks. We evaluate the performance of our approach against baselines and identify insights throughout this paper.

Zero-inflated datasets, which have an excess of zero outputs, are commonly encountered in problems such as climate or rare event modelling. Conventional machine learning approaches tend to overestimate the non-zeros leading to poor performance. We propose a novel model family of zero-inflated Gaussian processes (ZiGP) for such zero-inflated datasets, produced by sparse kernels through learning a latent probit Gaussian process that can zero out kernel rows and columns whenever the signal is absent. The ZiGPs are particularly useful for making the powerful Gaussian process networks more interpretable. We introduce sparse GP networks where variable-order latent modelling is achieved through sparse mixing signals. We derive the nontrivial stochastic variational inference tractably for scalable learning of the sparse kernels in both models. The novel output-sparse approach improves both prediction of zero-inflated data and inter-pretability of latent mixing models.

We present the Structural Agnostic Model (SAM), a framework to estimate end-to-end non-acyclic causal graphs from observational data. In a nutshell, SAM implements an adversarial game in which a separate model generates each variable, given real values from all others. In tandem, a discriminator attempts to distinguish between the joint distributions of real and generated samples. Finally, a sparsity penalty forces each generator to consider only a small subset of the variables, yielding a sparse causal graph. SAM scales easily to hundreds variables. Our experiments show the state-of-the-art performance of SAM on discovering causal structures and modeling interventions, in both acyclic and non-acyclic graphs.

Low-rank approximations of data matrices are an important dimensionality reduction tool in machine learning and regression analysis. We consider the case of categorical variables, where it can be formulated as the problem of finding low-rank approximations to Boolean matrices. In this paper we give what is to the best of our knowledge the first integer programming formulation that relies on only polynomially many variables and constraints, we discuss how to solve it computationally and report numerical tests on synthetic and real-world data.

Deep neural networks (DNNs) enable innovative applications of machine learning like image recognition, machine translation, or malware detection. However, deep learning is often criticized for its lack of robustness in adversarial settings (e.g., vulnerability to adversarial inputs) and general inability to rationalize its predictions. In this work, we exploit the structure of deep learning to enable new learning-based inference and decision strategies that achieve desirable properties such as robustness and interpretability. We take a first step in this direction and introduce the Deep k-Nearest Neighbors (DkNN). This hybrid classifier combines the k-nearest neighbors algorithm with representations of the data learned by each layer of the DNN: a test input is compared to its neighboring training points according to the distance that separates them in the representations. We show the labels of these neighboring points afford confidence estimates for inputs outside the model's training manifold, including on malicious inputs like adversarial examples--and therein provides protections against inputs that are outside the models understanding. This is because the nearest neighbors can be used to estimate the nonconformity of, i.e., the lack of support for, a prediction in the training data. The neighbors also constitute human-interpretable explanations of predictions. We evaluate the DkNN algorithm on several datasets, and show the confidence estimates accurately identify inputs outside the model, and that the explanations provided by nearest neighbors are intuitive and useful in understanding model failures.

A matrix completion problem, which aims to recover a complete matrix from its partial observations, is one of the important problems in the machine learning field and has been studied actively. However, there is a discrepancy between the mainstream problem setting, which assumes continuous-valued observations, and some practical applications such as recommendation systems and SNS link predictions where observations take discrete or even binary values. To cope with this problem, Davenport et al. (2014) proposed a binary matrix completion (BMC) problem, where observations are quantized into binary values. Hsieh et al. (2015) proposed a PU (Positive and Unlabeled) matrix completion problem, which is an extension of the BMC problem. This problem targets the setting where we cannot observe negative values, such as SNS link predictions. In the construction of their method for this setting, they introduced a methodology of the classification problem, regarding each matrix entry as a sample. Their risk, which defines losses over unobserved entries as well, indicates the possibility of the use of unobserved entries. In this paper, motivated by a semi-supervised classification method recently proposed by Sakai et al. (2017), we develop a method for the BMC problem which can use all of positive, negative, and unobserved entries, by combining the risks of Davenport et al. (2014) and Hsieh et al. (2015). To the best of our knowledge, this is the first BMC method which exploits all kinds of matrix entries. We experimentally show that an appropriate mixture of risks improves the performance.

Parameter inference for stochastic differential equations is challenging due to the presence of a latent diffusion process. Working with an Euler-Maruyama discretisation for the diffusion, we use variational inference to jointly learn the parameters and the diffusion paths. We use a standard mean-field variational approximation of the parameter posterior, and introduce a recurrent neural network to approximate the posterior for the diffusion paths conditional on the parameters. This neural network learns how to provide Gaussian state transitions which bridge between observations in a very similar way to the conditioned diffusion process. The resulting black-box inference method can be applied to any SDE system with light tuning requirements. We illustrate the method on a Lotka-Volterra system and an epidemic model, producing accurate parameter estimates in a few hours.

Period estimation is one of the central topics in astronomical time series analysis, where data is often unevenly sampled. Especially challenging are studies of stellar magnetic cycles, as there the periods looked for are of the order of the same length than the datasets themselves. The datasets often contain trends, the origin of which is either a real long-term cycle or an instrumental effect, but these effects cannot be reliably separated, while they can lead to erroneous period determinations if not properly handled. In this study we aim at developing a method that can handle the trends properly, and by performing extensive set of testing, we show that this is the optimal procedure when contrasted with methods that do not include the trend directly to the model. The effect of the form of the noise (whether constant or heteroscedastic) on the results is also investigated. We introduce a Bayesian Generalised Lomb-Scargle Periodogram with Trend (BGLST), which is a probabilistic linear regression model using Gaussian priors for the coefficients and uniform prior for the frequency parameter. We show, using synthetic data, that when there is no prior information on whether and to what extent the true model of the data contains a linear trend, the introduced BGLST method is preferable to the methods which either detrend the data or leave the data untrended before fitting the periodic model. Whether to use noise with different than constant variance in the model depends on the density of the data sampling as well as on the true noise type of the process.

Early stopping of iterative algorithms is a widely-used form of regularization in statistics, commonly used in conjunction with boosting and related gradient-type algorithms. Although consistency results have been established in some settings, such estimators are less well-understood than their analogues based on penalized regularization. In this paper, for a relatively broad class of loss functions and boosting algorithms (including L2-boost, LogitBoost and AdaBoost, among others), we exhibit a direct connection between the performance of a stopped iterate and the localized Gaussian complexity of the associated function class. This connection allows us to show that local fixed point analysis of Gaussian or Rademacher complexities, now standard in the analysis of penalized estimators, can be used to derive optimal stopping rules. We derive such stopping rules in detail for various kernel classes, and illustrate the correspondence of our theory with practice for Sobolev kernel classes.

We propose a fast method with statistical guarantees for learning an exponential family density model where the natural parameter is in a reproducing kernel Hilbert space, and may be infinite-dimensional. The model is learned by fitting the derivative of the log density, the score, thus avoiding the need to compute a normalization constant. Our approach improves the computational efficiency of an earlier solution by using a low-rank, Nystr\"om-like solution. The new solution retains the consistency and convergence rates of the full-rank solution (exactly in Fisher distance, and nearly in other distances), with guarantees on the degree of cost and storage reduction. We evaluate the method in experiments on density estimation and in the construction of an adaptive Hamiltonian Monte Carlo sampler. Compared to an existing score learning approach using a denoising autoencoder, our estimator is empirically more data-efficient when estimating the score, runs faster, and has fewer parameters (which can be tuned in a principled and interpretable way), in addition to providing statistical guarantees.