First, and arguably the most popular type of machine learning algorithm, is linear regression. Linear regression algorithms map simple correlations between two variables in a set of data. A set of inputs and their corresponding outputs are examined and quantified to show a relationship, including how a change in one variable affects the other. Linear regressions are plotted via a line on a graph. Linear regression's popularity is due to its simplicity: The algorithm is easily explainable, relatively transparent and requires little to no parameter tuning.

Linking facts across documents is a challenging task, as the language used to express the same information in a sentence can vary significantly, which complicates the task of multi-document summarization. Consequently, existing approaches heavily rely on hand-crafted features, which are domain-dependent and hard to craft, or additional annotated data, which is costly to gather. To overcome these limitations, we present a novel method, which makes use of two types of sentence embeddings: universal embeddings, which are trained on a large unrelated corpus, and domain-specific embeddings, which are learned during training. To this end, we develop SemSentSum, a fully data-driven model able to leverage both types of sentence embeddings by building a sentence semantic relation graph. SemSentSum achieves competitive results on two types of summary, consisting of 665 bytes and 100 words. Unlike other state-of-the-art models, neither hand-crafted features nor additional annotated data are necessary, and the method is easily adaptable for other tasks. To our knowledge, we are the first to use multiple sentence embeddings for the task of multi-document summarization.

Large textual corpora are often represented by the document-term frequency matrix whose elements are the frequency of terms; however, this matrix has two problems: sparsity and high dimensionality. Four dimension reduction strategies are used to address these problems. Of the four strategies, unsupervised feature transformation (UFT) is a popular and efficient strategy to map the terms to a new basis in the document-term frequency matrix. Although several UFT-based methods have been developed, fuzzy clustering has not been considered for dimensionality reduction. This research explores fuzzy clustering as a new UFT-based approach to create a lower-dimensional representation of documents. Performance of fuzzy clustering with and without using global term weighting methods is shown to exceed principal component analysis and singular value decomposition. This study also explores the effect of applying different fuzzifier values on fuzzy clustering for dimensionality reduction purpose.

A body of recent work has focused on constructing a variational family of filtered distributions using Sequential Monte Carlo (SMC). Inspired by this work, we introduce Particle Smoothing Variational Objectives (SVO), a novel backward simulation technique and smoothed approximate posterior defined through a subsampling process. SVO augments support of the proposal and boosts particle diversity. Recent literature argues that increasing the number of samples K to obtain tighter variational bounds may hurt the proposal learning, due to a signal-to-noise ratio (SNR) of gradient estimators decreasing at the rate $\mathcal{O}(1/\sqrt{K})$. As a second contribution, we develop theoretical and empirical analysis of the SNR in filtering SMC, which motivates our choice of biased gradient estimators. We prove that introducing bias by dropping Categorical terms from the gradient estimate or using Gumbel-Softmax mitigates the adverse effect on the SNR. We apply SVO to three nonlinear latent dynamics tasks and provide statistics to rigorously quantify the predictions of filtered and smoothed objectives. SVO consistently outperforms filtered objectives when given fewer Monte Carlo samples on three nonlinear systems of increasing complexity.

Hierarchical clustering is a widely used approach for clustering datasets at multiple levels of granularity. Despite its popularity, existing algorithms such as hierarchical agglomerative clustering (HAC) are limited to the offline setting, and thus require the entire dataset to be available. This prohibits their use on large datasets commonly encountered in modern learning applications. In this paper, we consider hierarchical clustering in the online setting, where points arrive one at a time. We propose two algorithms that seek to optimize the Moseley and Wang (MW) revenue function, a variant of the Dasgupta cost. These algorithms offer different tradeoffs between efficiency and MW revenue performance. The first algorithm, OTD, is a highly efficient Online Top Down algorithm which provably achieves a 1/3-approximation to the MW revenue under a data separation assumption. The second algorithm, OHAC, is an online counterpart to offline HAC, which is known to yield a 1/3-approximation to the MW revenue, and produce good quality clusters in practice. We show that OHAC approximates offline HAC by leveraging a novel split-merge procedure. We empirically show that OTD and OHAC offer significant efficiency and cluster quality gains respectively over baselines.

Sepsis is the leading cause of death in non-coronary intensive care units. Moreover, a delay of antibiotic treatment of patients with severe sepsis by only few hours is associated with increased mortality. This insight makes accurate models for early prediction of sepsis a key task in machine learning for healthcare. Previous approaches have achieved high AUROC by learning from electronic health records where sepsis labels were defined automatically following established clinical criteria. We argue that the practice of incorporating the clinical criteria that are used to automatically define ground truth sepsis labels as features of severity scoring models is inherently circular and compromises the validity of the proposed approaches. We propose to create an independent ground truth for sepsis research by exploiting implicit knowledge of clinical practitioners via an electronic questionnaire which records attending physicians' daily judgements of patients' sepsis status. We show that despite its small size, our dataset allows to achieve state-of-the-art AUROC scores. An inspection of learned weights for standardized features of the linear model lets us infer potentially surprising feature contributions and allows to interpret seemingly counterintuitive findings.

We provide high probability sample complexity guarantees for non-parametric structure learning of tree-shaped graphical models whose nodes are discrete random variables with a finite or countable alphabet, both in the noiseless and noisy regimes. First, we introduce a new, fundamental quantity called the (noisy) information threshold, which arises naturally from the error analysis of the Chow-Liu algorithm and characterizes not only the sample complexity, but also the inherent impact of the noise on the structure learning task, without explicit assumptions on the distribution of the model. This allows us to present the first non-parametric, high-probability finite sample complexity bounds on tree-structure learning from potentially noise-corrupted data. In particular, for number of nodes $p$, success rate $1-\delta$, and a fixed value of the information threshold, our sample complexity bounds for exact structure recovery are of the order of $\mathcal{O}\big(\log^{1+\zeta} (p/\delta)\big) $, for all $\zeta>0$, for both noiseless and noisy settings. Subsequently, we apply our results on two classes of hidden models, namely, the $M$-ary erasure channel and the generalized symmetric channel, illustrating the usefulness and importance of our framework. As a byproduct of our analysis, this paper resolves the open problem of tree structure learning in the presence of non-identically distributed observation noise, providing explicit conditions on the convergence of the Chow-Liu algorithm under this setting as well.

We introduce a framework to study the transformation of problems with manifold constraints into unconstrained problems through parametrizations in terms of a Euclidean space. We call these parametrizations "trivializations". We prove conditions under which a trivialization is sound in the context of gradient-based optimization and we show how two large families of trivializations have overall favorable properties, but also suffer from a performance issue. We then introduce "dynamic trivializations", which solve this problem, and we show how these form a family of optimization methods that lie between trivializations and Riemannian gradient descent, and combine the benefits of both of them. We then show how to implement these two families of trivializations in practice for different matrix manifolds. To this end, we prove a formula for the gradient of the exponential of matrices, which can be of practical interest on its own. Finally, we show how dynamic trivializations improve the performance of existing methods on standard tasks designed to test long-term memory within neural networks.

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies on judiciously combining a large number of computationally cheap training data on coarse resolutions with a few expensive training samples on fine grid resolutions. Theoretical arguments for lowering the generalization error, based on reducing the variance of the underlying maps, are provided and numerical evidence, indicating significant gains over underlying single-level machine learning algorithms, are presented. Moreover, we also apply the multi-level algorithm in the context of forward uncertainty quantification and observe a considerable speed-up over competing algorithms.

Metaheuristic algorithms (MAs) have seen unprecedented growth thanks to their successful applications in fields including engineering and health sciences. In this work, we investigate the use of a deep learning (DL) model as an alternative tool to do so. The proposed method, called MaNet, is motivated by the fact that most of the DL models often need to solve massive nasty optimization problems consisting of millions of parameters. Feature selection is the main adopted concepts in MaNet that helps the algorithm to skip irrelevant or partially relevant evolutionary information and uses those which contribute most to the overall performance. The introduced model is applied on several unimodal and multimodal continues problems. The experiments indicate that MaNet is able to yield competitive results compared to one of the best hand-designed algorithms for the aforementioned problems, in terms of the solution accuracy and scalability.