We study the sample-based $k$-median clustering objective under a sequential setting without substitutions. In this setting, the goal is to select k centers that approximate the optimal clustering on an unknown distribution from a finite sequence of i.i.d. samples, where any selection of a center must be done immediately after the center is observed and centers cannot be substituted after selection. We provide an efficient algorithm for this setting, and show that its multiplicative approximation factor is twice the approximation factor of an efficient offline algorithm. In addition, we show that if efficiency requirements are removed, there is an algorithm that can obtain the same approximation factor as the best offline algorithm.

Predicting not only the target but also an accurate measure of uncertainty is important for many applications and in particular safety-critical ones. In this work we study the calibration of uncertainty prediction for regression tasks which often arise in real-world systems. We show that the existing approach for evaluating the calibration of a regression uncertainty [Kuleshov et al. 2018] has severe limitations in distinguishing informative from non-informative uncertainty predictions. We propose a new evaluation method that escapes this caveat using a simple histogram-based approach inspired by reliability diagrams used in classification tasks. Our method clusters examples with similar uncertainty prediction and compares the prediction with the empirical uncertainty on these examples. We also propose a simple scaling-based calibration that preforms well in our experimental tests. We show results on both a synthetic, controlled problem and on the object detection bounding-box regression task using the COCO and KITTI datasets.

Deep (neural) networks have been applied productively in a wide range of supervised and unsupervised learning tasks. Unlike classical machine learning algorithms, deep networks typically operate in the overparameterized regime, where the number of parameters is larger than the number of training data points. Consequently, understanding the generalization properties and role of (explicit or implicit) regularization in these networks is of great importance. Inspired by the seminal work of Donoho and Grimes in manifold learning, we develop a new measure for the complexity of the function generated by a deep network based on the integral of the norm of the tangent Hessian. This complexity measure can be used to quantify the irregularity of the function a deep network fits to training data or as a regularization penalty for deep network learning. Indeed, we show that the oft-used heuristic of data augmentation imposes an implicit Hessian regularization during learning. We demonstrate the utility of our new complexity measure through a range of learning experiments.

The 2016 United States presidential election has been characterized as a period of extreme divisiveness that was exacerbated on social media by the influence of fake news, trolls, and social bots. However, the extent to which the public became more polarized in response to these influences over the course of the election is not well understood. In this paper we propose IdeoTrace, a framework for (i) jointly estimating the ideology of social media users and news websites and (ii) tracing changes in user ideology over time. We apply this framework to the last two months of the election period for a group of 47508 Twitter users and demonstrate that both liberal and conservative users became more polarized over time.

Although "black box" models such as Artificial Neural Networks, Support Vector Machines, and Ensemble Approaches continue to show superior performance in many disciplines, their adoption in the sensitive disciplines (e.g., finance, healthcare) is questionable due to the lack of interpretability and explainability of the model. In fact, future adoption of "black box" models is difficult because of the recent rule of "right of explanation" by the European Union where a user can ask for an explanation behind an algorithmic decision, and the newly proposed bill by the US government, the "Algorithmic Accountability Act", which would require companies to assess their machine learning systems for bias and discrimination and take corrective measures. Top Bankruptcy Prediction Models are A.I.-based and are in need of better explainability -the extent to which the internal working mechanisms of an AI system can be explained in human terms. Although explainable artificial intelligence is an emerging field of research, infusing domain knowledge for better explainability might be a possible solution. In this work, we demonstrate a way to collect and infuse domain knowledge into a "black box" model for bankruptcy prediction. Our understanding from the experiments reveals that infused domain knowledge makes the output from the black box model more interpretable and explainable.

Many of us do not know that there is a proper list of machine learning algorithms. So here in this article, we will see some methods of using these algorithms. Through these Machine learning algorithm, you also get to know more about Artificial intelligence and designing machine learning system. These are the most important Algorithms in Machine Learning. If you are aware of these Algorithms then you can use them well to apply in almost any Data Problem.

The article describes our submission to SemEval 2019 Task 8 on Fact-Checking in Community Forums. The systems under discussion participated in Subtask A: decide whether a question asks for factual information, opinion/advice or is just socializing. Our primary submission was ranked as the second one among all participants in the official evaluation phase. The article presents our primary solution: Deeply Regularized Residual Neural Network (DRR NN) with Universal Sentence Encoder embeddings. This is followed by a description of two contrastive solutions based on ensemble methods.

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may significantly vary between different points. (For example, the algorithm will use larger $k$ for predicting the labels of points in noisy regions.) We provide theory and experiments that demonstrate that the algorithm performs comparably to, and sometimes better than, $k$-NN with an optimal choice of $k$. In particular, we derive bounds on the convergence rates of our classifier that depend on a local quantity we call the `advantage' which is significantly weaker than the Lipschitz conditions used in previous convergence rate proofs. These generalization bounds hinge on a variant of the seminal Uniform Convergence Theorem due to Vapnik and Chervonenkis; this variant concerns conditional probabilities and may be of independent interest.

Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo sampling algorithm for drawing samples from smooth probability densities over continuous spaces. We study the variant most widely used in practice, Metropolized HMC with the St\"{o}rmer-Verlet or leapfrog integrator, and make two primary contributions. First, we provide a non-asymptotic upper bound on the mixing time of the Metropolized HMC with explicit choices of stepsize and number of leapfrog steps. This bound gives a precise quantification of the faster convergence of Metropolized HMC relative to simpler MCMC algorithms such as the Metropolized random walk, or Metropolized Langevin algorithm. Second, we provide a general framework for sharpening mixing time bounds Markov chains initialized at a substantial distance from the target distribution over continuous spaces. We apply this sharpening device to the Metropolized random walk and Langevin algorithms, thereby obtaining improved mixing time bounds from a non-warm initial distribution.

We consider the problem of selecting the best estimator among a family of Tikhonov regularized estimators, or, alternatively, to select a linear combination of these regularizers that is as good as the best regularizer in the family. Our theory reveals that if the Tikhonov regularizers share the same penalty matrix with different tuning parameters, a convex procedure based on $Q$-aggregation achieves the mean square error of the best estimator, up to a small error term no larger than $C\sigma^2$, where $\sigma^2$ is the noise level and $C>0$ is an absolute constant. Remarkably, the error term does not depend on the penalty matrix or the number of estimators as long as they share the same penalty matrix, i.e., it applies to any grid of tuning parameters, no matter how large the cardinality of the grid is. This reveals the surprising "cost-free" nature of optimally tuning Tikhonov regularizers, in striking contrast with the existing literature on aggregation of estimators where one typically has to pay a cost of $\sigma^2\log(M)$ where $M$ is the number of estimators in the family. The result holds, more generally, for any family of ordered linear smoothers. This encompasses Ridge regression as well as Principal Component Regression. The result is extended to the problem of tuning Tikhonov regularizers with different penalty matrices.