Archetypal analysis approximates data by means of mixtures of actual extreme cases (archetypoids) or archetypes, which are a convex combination of cases in the data set. Archetypes lie on the boundary of the convex hull. This makes the analysis very sensitive to outliers. A robust methodology by means of M-estimators for classical multivariate and functional data is proposed. This unsupervised methodology allows complex data to be understood even by non-experts. The performance of the new procedure is assessed in a simulation study, where a comparison with a previous methodology for the multivariate case is also carried out, and our proposal obtains favorable results. Finally, robust bivariate functional archetypoid analysis is applied to a set of companies in the S\&P 500 described by two time series of stock quotes. A new graphic representation is also proposed to visualize the results. The analysis shows how the information can be easily interpreted and how even non-experts can gain a qualitative understanding of the data.

In this paper, we propose a deep, globally normalized topic model that incorporates structural relationships connecting documents in socially generated corpora, such as online forums. Our model (1) captures discursive interactions along observed reply links in addition to traditional topic information, and (2) incorporates latent distributed representations arranged in a deep architecture, which enables a GPU-based mean-field inference procedure that scales efficiently to large data. We apply our model to a new social media dataset consisting of 13M comments mined from the popular internet forum Reddit, a domain that poses significant challenges to models that do not account for relationships connecting user comments. We evaluate against existing methods across multiple metrics including perplexity and metadata prediction, and qualitatively analyze the learned interaction patterns.

We present a study on predicting the factuality of reporting and bias of news media. While previous work has focused on studying the veracity of claims or documents, here we are interested in characterizing entire news media. These are under-studied but arguably important research problems, both in their own right and as a prior for fact-checking systems. We experiment with a large list of news websites and with a rich set of features derived from (i) a sample of articles from the target news medium, (ii) its Wikipedia page, (iii) its Twitter account, (iv) the structure of its URL, and (v) information about the Web traffic it attracts. The experimental results show sizable performance gains over the baselines, and confirm the importance of each feature type.

We present an approach based on machine learning (ML) to distinguish eruption and precursory signals of Chimay\'{o} geyser (New Mexico, USA) under noisy environments. This geyser can be considered as a natural analog of $\mathrm{CO}_2$ intrusion into shallow water aquifers. By studying this geyser, we can understand upwelling of $\mathrm{CO}_2$-rich fluids from depth, which has relevance to leak monitoring in a $\mathrm{CO}_2$ sequestration project. ML methods such as Random Forests (RF) are known to be robust multi-class classifiers and perform well under unfavorable noisy conditions. However, the extent of the RF method's accuracy is poorly understood for this $\mathrm{CO}_2$-driven geysering application. The current study aims to quantify the performance of RF-classifiers to discern the geyser state. Towards this goal, we first present the data collected from the seismometer that is installed near the Chimay\'{o} geyser. The seismic signals collected at this site contain different types of noises such as daily temperature variations, seasonal trends, animal movement near the geyser, and human activity. First, we filter the signals from these noises by combining the Butterworth-Highpass filter and an Autoregressive method in a multi-level fashion. We show that by combining these filtering techniques, in a hierarchical fashion, leads to reduction in the noise in the seismic data without removing the precursors and eruption event signals. We then use RF on the filtered data to classify the state of geyser into three classes -- remnant noise, precursor, and eruption states. We show that the classification accuracy using RF on the filtered data is greater than 90\%.These aspects make the proposed ML framework attractive for event discrimination and signal enhancement under noisy conditions, with strong potential for application to monitoring leaks in $\mathrm{CO}_2$ sequestration.

We present a powerful new loss function and training scheme for learning binary hash codes with any differentiable model and similarity function. Our loss function improves over prior methods by using log likelihood loss on top of an accurate approximation for the probability that two inputs fall within a Hamming distance target. Our novel training scheme obtains a good estimate of the true gradient by better sampling inputs and evaluating loss terms between all pairs of inputs in each minibatch. To fully leverage the resulting hashes, we use multi-indexing. We demonstrate that these techniques provide large improvements to a similarity search tasks. We report the best results to date on competitive information retrieval tasks for ImageNet and SIFT 1M, improving MAP from 73% to 84% and reducing query cost by a factor of 2-8, respectively.

We study the problem of optimizing a function under a \emph{budgeted number of evaluations}. We only assume that the function is \emph{locally} smooth around one of its global optima. The difficulty of optimization is measured in terms of 1) the amount of \emph{noise} $b$ of the function evaluation and 2) the local smoothness, $d$, of the function. A smaller $d$ results in smaller optimization error. We come with a new, simple, and parameter-free approach. First, for all values of $b$ and $d$, this approach recovers at least the state-of-the-art regret guarantees. Second, our approach additionally obtains these results while being \textit{agnostic} to the values of both $b$ and $d$. This leads to the first algorithm that naturally adapts to an \textit{unknown} range of noise $b$ and leads to significant improvements in a moderate and low-noise regime. Third, our approach also obtains a remarkable improvement over the state-of-the-art \SOO algorithm when the noise is very low which includes the case of optimization under deterministic feedback ($b=0$). There, under our minimal local smoothness assumption, this improvement is of exponential magnitude and holds for a class of functions that covers the vast majority of functions that practitioners optimize ($d=0$). We show that our algorithmic improvement is also borne out in the numerical experiments, where we empirically show faster convergence on common benchmark functions.

Regression-via-Classification (RvC) is the process of converting a regression problem to a classification one. Current approaches for RvC use ad-hoc discretization strategies and are suboptimal. We propose a neural regression tree model for RvC. In this model, we employ a joint optimization framework where we learn optimal discretization thresholds while simultaneously optimizing the features for each node in the tree. We empirically show the validity of our model by testing it on two challenging regression tasks where we establish the state of the art.

In conventional binary classification, examples are labeled as either positive (P) or negative (N), and we train a classifier on these labeled examples. On the contrary, positive-unlabeled (PU) learning addresses the problem of learning a classifier from P and unlabeled (U) data, without need of explicitly identifying N data (Elkan & Noto, 2008; Ward et al., 2009). PU learning finds its usefulness in many real-world problems. For example, in one-class remote sensing classification (Li et al., 2011), we seek to extract a specific land-cover class from an image. While it is easy to label examples of this specific land-cover class of interest, examples not belonging to this class are too diverse to be exhaustively annotated. The same problem arises in text classification, as it is difficult or even impossible to compile a set of N samples that provides a comprehensive characterization of everything that is not in the P class (Liu et al., 2003; Fung et al., 2006). Besides, PU learning has also been applied to other domains such as outlier detection (Hido et al., 2008; Scott & Blanchard, 2009), medical diagnosis (Zuluaga et al., 2011), or time series classification (Nguyen et al., 2011). By carefully examining the above examples, we find out that the most difficult step is often to collect a fully representative N set, whereas only labeling a small portion of all possible N data is relatively easy. Therefore, in this paper, we propose to study the problem of learning from P, U and biased N (bN) data, which we name PUbN learning hereinafter.

A line of recent work has characterized the behavior of the EM algorithm in favorable settings in which the population likelihood is locally strongly concave around its maximizing argument. Examples include suitably separated Gaussian mixture models and mixtures of linear regressions. We consider instead over-fitted settings in which the likelihood need not be strongly concave, or, equivalently, when the Fisher information matrix might be singular. In such settings, it is known that a global maximum of the MLE based on $n$ samples can have a non-standard $n^{-1/4}$ rate of convergence. How does the EM algorithm behave in such settings? Focusing on the simple setting of a two-component mixture fit to a multivariate Gaussian distribution, we study the behavior of the EM algorithm both when the mixture weights are different (unbalanced case), and are equal (balanced case). Our analysis reveals a sharp distinction between these cases: in the former, the EM algorithm converges geometrically to a point at Euclidean distance $O((d/n)^{1/2})$ from the true parameter, whereas in the latter case, the convergence rate is exponentially slower, and the fixed point has a much lower $O((d/n)^{1/4})$ accuracy. The slower convergence in the balanced over-fitted case arises from the singularity of the Fisher information matrix. Analysis of this singular case requires the introduction of some novel analysis techniques, in particular we make use of a careful form of localization in the associated empirical process, and develop a recursive argument to progressively sharpen the statistical rate.

Many machine learning tasks such as multiple instance learning, 3D shape recognition and few-shot image classification are defined on sets of instances. Since solutions to such problems do not depend on the permutation of elements of the set, models used to address them should be permutation invariant. We present an attention-based neural network module, the Set Transformer, specifically designed to model interactions among elements in the input set. The model consists of an encoder and a decoder, both of which rely on attention mechanisms. In an effort to reduce computational complexity, we introduce an attention scheme inspired by inducing point methods from sparse Gaussian process literature. It reduces computation time of self-attention from quadratic to linear in the number of elements in the set. We show that our model is theoretically attractive and we evaluate it on a range of tasks, demonstrating increased performance compared to recent methods for set-structured data. Learning representations has proven to be an essential problem for deep learning and its many success stories. The majority of problems tackled by deep learning are instance-based and take the form of mapping a fixed-dimensional input tensor to its corresponding target value (Krizhevsky et al., 2012; Graves et al., 2013). For some applications, we are required to process set-structured data.