This work introduces a new unsupervised representation learning technique called Deep Convolutional Transform Learning (DCTL). By stacking convolutional transforms, our approach is able to learn a set of independent kernels at different layers. The features extracted in an unsupervised manner can then be used to perform machine learning tasks, such as classification and clustering. The learning technique relies on a well-sounded alternating proximal minimization scheme with established convergence guarantees. Our experimental results show that the proposed DCTL technique outperforms its shallow version CTL, on several benchmark datasets.

We study a framework of regularized $K$-means methods based on direct penalization of the size of the cluster centers. Different penalization strategies are considered and compared through simulation and theoretical analysis. Based on the results, we propose HT $K$-means, which uses an $\ell_0$ penalty to induce sparsity in the variables. Different techniques for selecting the tuning parameter are discussed and compared. The proposed method stacks up favorably with the most popular regularized $K$-means methods in an extensive simulation study. Finally, HT $K$-means is applied to several real data examples. Graphical displays are presented and used in these examples to gain more insight into the datasets.

Entities are at the center of how we represent and aggregate knowledge. For instance, Encyclopedias such as Wikipedia are structured by entities (e.g., one per article). The ability to retrieve such entities given a query is fundamental for knowledge-intensive tasks such as entity linking and open-domain question answering. One way to understand current approaches is as classifiers among atomic labels, one for each entity. Their weight vectors are dense entity representations produced by encoding entity information such as descriptions. This approach leads to several shortcomings: i) context and entity affinity is mainly captured through a vector dot product, potentially missing fine-grained interactions between the two; ii) a large memory footprint is needed to store dense representations when considering large entity sets; iii) an appropriately hard set of negative data has to be subsampled at training time. We propose GENRE, the first system that retrieves entities by generating their unique names, left to right, token-by-token in an autoregressive fashion, and conditioned on the context. This enables to mitigate the aforementioned technical issues: i) the autoregressive formulation allows us to directly capture relations between context and entity name, effectively cross encoding both; ii) the memory footprint is greatly reduced because the parameters of our encoder-decoder architecture scale with vocabulary size, not entity count; iii) the exact softmax loss can be efficiently computed without the need to subsample negative data. We show the efficacy of the approach with more than 20 datasets on entity disambiguation, end-to-end entity linking and document retrieval tasks, achieving new SOTA, or very competitive results while using a tiny fraction of the memory of competing systems. Finally, we demonstrate that new entities can be added by simply specifying their unambiguous name.

Stochastic optimization lies at the heart of machine learning, and its cornerstone is stochastic gradient descent (SGD), a method introduced over 60 years ago. The last 8 years have seen an exciting new development: variance reduction (VR) for stochastic optimization methods. These VR methods excel in settings where more than one pass through the training data is allowed, achieving a faster convergence than SGD in theory as well as practice. These speedups underline the surge of interest in VR methods and the fast-growing body of work on this topic. This review covers the key principles and main developments behind VR methods for optimization with finite data sets and is aimed at non-expert readers. We focus mainly on the convex setting, and leave pointers to readers interested in extensions for minimizing non-convex functions.

A vital aspect of the classification based model construction process is the calibration of the scoring function. One of the weaknesses of the calibration process is that it does not take into account the information about the relative positions of the recognized objects in the feature space. To alleviate this limitation, in this paper, we propose a novel concept of calculating a scoring function based on the distance of the object from the decision boundary and its distance to the class centroid. An important property is that the proposed score function has the same nature for all linear base classifiers, which means that outputs of these classifiers are equally represented and have the same meaning. The proposed approach is compared with other ensemble algorithms and experiments on multiple Keel datasets demonstrate the effectiveness of our method. To discuss the results of our experiments, we use multiple classification performance measures and statistical analysis.

The field of Astronomy requires the collection and assimilation of vast volumes of data. The data handling and processing problem has become severe as the sheer volume of data produced by scientific instruments each night grows exponentially. This problem becomes extensive for conventional methods of processing the data, which was mostly manual, but is the perfect setting for the use of Machine Learning approaches. While building classifiers for Astronomy, the cost of losing a rare object like supernovae or quasars to detection losses is far more severe than having many false positives, given the rarity and scientific value of these objects. In this paper, a Linear Support Vector Machine (LSVM) is explored to detect Quasars, which are extremely bright objects in which a supermassive black hole is surrounded by a luminous accretion disk. In Astronomy, it is vital to correctly identify quasars, as they are very rare in nature. Their rarity creates a class-imbalance problem that needs to be taken into consideration. The class-imbalance problem and high cost of misclassification are taken into account while designing the classifier. To achieve this detection, a novel classifier is explored, and its performance is evaluated. It was observed that LSVM along with Ensemble Bagged Trees (EBT) achieved a 10x reduction in the False Negative Rate, using the Learning from Mistakes methodology.

Federated learning (FL) is a framework for distributed learning of centralized models. In FL, a set of edge devices train a model using their local data, while repeatedly exchanging their trained updates with a central server. This procedure allows tuning a centralized model in a distributed fashion without having the users share their possibly private data. In this paper, we focus on over-the-air (OTA) FL, which has been suggested recently to reduce the communication overhead of FL due to the repeated transmissions of the model updates by a large number of users over the wireless channel. In OTA FL, all users simultaneously transmit their updates as analog signals over a multiple access channel, and the server receives a superposition of the analog transmitted signals. However, this approach results in the channel noise directly affecting the optimization procedure, which may degrade the accuracy of the trained model. We develop a Convergent OTA FL (COTAF) algorithm which enhances the common local stochastic gradient descent (SGD) FL algorithm, introducing precoding at the users and scaling at the server, which gradually mitigates the effect of the noise. We analyze the convergence of COTAF to the loss minimizing model and quantify the effect of a statistically heterogeneous setup, i.e. when the training data of each user obeys a different distribution. Our analysis reveals the ability of COTAF to achieve a convergence rate similar to that achievable over error-free channels. Our simulations demonstrate the improved convergence of COTAF over vanilla OTA local SGD for training using non-synthetic datasets. Furthermore, we numerically show that the precoding induced by COTAF notably improves the convergence rate and the accuracy of models trained via OTA FL.

In this work, we study asynchronous finite sum minimization in a distributed-data setting with a central parameter server. While asynchrony is well understood in parallel settings where the data is accessible by all machines, little is known for the distributed-data setting. We introduce a variant of SAGA called ADSAGA for the distributed-data setting where each machine stores a partition of the data. We show that with independent exponential work times -- a common assumption in distributed optimization -- ADSAGA converges in $\tilde{O}\left(\left(n + \sqrt{m}\kappa\right)\log(1/\epsilon)\right)$ iterations, where $n$ is the number of component functions, $m$ is the number of machines, and $\kappa$ is a condition number. We empirically compare the iteration complexity of ADSAGA to existing parallel and distributed algorithms, including synchronous mini-batch algorithms.

The preponderance of large-scale healthcare databases provide abundant opportunities for comparative effectiveness research. Evidence necessary to making informed treatment decisions often relies on comparing effectiveness of multiple treatment options on outcomes of interest observed in a small number of individuals. Causal inference with multiple treatments and rare outcomes is a subject that has been treated sparingly in the literature. This paper designs three sets of simulations, representative of the structure of our healthcare database study, and propose causal analysis strategies for such settings. We investigate and compare the operating characteristics of three types of methods and their variants: Bayesian Additive Regression Trees (BART), regression adjustment on multivariate spline of generalized propensity scores (RAMS) and inverse probability of treatment weighting (IPTW) with multinomial logistic regression or generalized boosted models. Our results suggest that BART and RAMS provide lower bias and mean squared error, and the widely used IPTW methods deliver unfavorable operating characteristics. We illustrate the methods using a case study evaluating the comparative effectiveness of robotic-assisted surgery, video-assisted thoracoscopic surgery and open thoracotomy for treating non-small cell lung cancer.

Many common loss functions such as mean-squared-error, cross-entropy, and reconstruction loss are unnecessarily rigid. Under a probabilistic interpretation, these common losses correspond to distributions with fixed shapes and scales. We instead argue for optimizing full likelihoods that include parameters like the normal variance and softmax temperature. Joint optimization of these "likelihood parameters" with model parameters can adaptively tune the scales and shapes of losses in addition to the strength of regularization. We explore and systematically evaluate how to parameterize and apply likelihood parameters for robust modeling, outlier-detection, and re-calibration. Additionally, we propose adaptively tuning $L_2$ and $L_1$ weights by fitting the scale parameters of normal and Laplace priors and introduce more flexible element-wise regularizers.