There is an immense literature focused on estimating the curvature of an unknown surface from point cloud dataset. Most existing algorithms estimate the curvature indirectly, that is, to estimate the surface locally by some basis functions and then calculate the curvature of such surface as an estimate of the curvature. Recently several methods have been proposed to estimate the curvature directly. However, these algorithms lack of theoretical guarantee on estimation error on small to moderate datasets. In this paper, we propose a direct and efficient method to estimate the curvature for oriented point cloud data without any surface approximation. In fact, we estimate the Weingarten map using a least square method, so that Gaussian curvature, mean curvature and principal curvatures can be obtained automatically from the Weingarten map. We show the convergence rate of our Weingarten Map Estimation (WME) algorithm is $n^{-2/3}$ both theoretically and numerically. Finally, we apply our method to point cloud simplification and surface reconstruction.

Algorithms typically come with tunable parameters that have a considerable impact on the computational resources they consume. Too often, practitioners must hand-tune the parameters, a tedious and error-prone task. A recent line of research provides algorithms that return nearly-optimal parameters from within a finite set. These algorithms can be used when the parameter space is infinite by providing as input a random sample of parameters. This data-independent discretization, however, might miss pockets of nearly-optimal parameters: prior research has presented scenarios where the only viable parameters lie within an arbitrarily small region. We provide an algorithm that learns a finite set of promising parameters from within an infinite set. Our algorithm can help compile a configuration portfolio, or it can be used to select the input to a configuration algorithm for finite parameter spaces. Our approach applies to any configuration problem that satisfies a simple yet ubiquitous structure: the algorithm's performance is a piecewise constant function of its parameters. Prior research has exhibited this structure in domains from integer programming to clustering. For these types of combinatorial problems, this is the first configuration algorithm beyond exhaustive search whose output provably competes with the best parameters from an infinite space.

The knowledge base completion problem is the problem of inferring missing information from existing facts in knowledge bases. Path-ranking based methods use sequences of relations as general patterns of paths for prediction. However, these patterns usually lack accuracy because they are generic and can often apply to widely varying scenarios. We leverage type hierarchies of entities to create a new class of path patterns that are both discriminative and generalizable. Then we propose an attention-based RNN model, which can be trained end-to-end, to discover the new path patterns most suitable for the data. Experiments conducted on two benchmark knowledge base completion datasets demonstrate that the proposed model outperforms existing methods by a statistically significant margin. Our quantitative analysis of the path patterns shows that they balance between generalization and discrimination.

Continuing my series on the UCI Heart Disease Data, is a tutorial on how to transform a logistic regression into a human transformable test. The tutorial can be found here. I talk about what logistic regression is, in addition to how to use it to make predictions.

A decision tree is a supervised machine learning model used to predict a target by learning decision rules from features. As the name suggests, we can think of this model as breaking down our data by making a decision based on asking a series of questions. Let's consider the following example in which we use a decision tree to decide upon an activity on a particular day: Based on the features in our training set, the decision tree model learns a series of questions to infer the class labels of the samples. As we can see, decision trees are attractive models if we care about interpretability. Although the preceding figure illustrates the concept of a decision tree based on categorical targets (classification), the same concept applies if our targets are real numbers (regression).

In a Data Science interview, the interviewer asked me, how would you explain top data science algorithms to a non-tech person. I told him that Data science is…..(read the article to know:D). The explanation is too simple that you can easily understand. We will discuss mostly machine learning algorithms that are important for data scientists and classify them based on supervised and unsupervised roles. I will provide you an outline for all the important algorithms that you can deploy for improving your data science operations. Here is the list of top Data Science Algorithms that you must know to become a data scientist.

Logistic regression is a traditional statistics technique that is also very popular as a machine learning tool. In this StatQuest, I go over the main ideas so that you can understand what it is and how it is used.

The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz [2001] is widely used for pricing American options. The LSM estimator contains undesirable look-ahead bias, and the conventional technique of removing it necessitates doubling simulations. We present the leave-one-out LSM (LOOLSM) algorithm for efficiently eliminating look-ahead bias. We validate the method with several option examples, including the multi-asset cases that the LSM algorithm significantly overvalues. We also obtain the convergence rates of look-ahead bias by measuring it using the LOOLSM method. The analysis and computational evidence support our findings.

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a long-standing gap between upper and lower bounds. Moreover, we show that our algorithm has faster finite-time and asymptotic rates on problems where the Bayes risk with respect to the square loss is small. We state our results using standard tools from the theory of least square regression in RKHSs, namely, the decay of the eigenvalues of the associated integral operator and the complexity of the optimal predictor measured through the integral operator.

Hyperbolic embeddings have recently gained attention in machine learning due to their ability to represent hierarchical data more accurately and succinctly than their Euclidean analogues. However, multi-relational knowledge graphs often exhibit multiple simultaneous hierarchies, which current hyperbolic models do not capture. To address this, we propose a model that embeds multi-relational graph data in the Poincar\'e ball model of hyperbolic space. Our Multi-Relational Poincar\'e model (MuRP) learns relation-specific parameters to transform entity embeddings by M\"obius matrix-vector multiplication and M\"obius addition. Experiments on the hierarchical WN18RR knowledge graph show that our multi-relational Poincar\'e embeddings outperform their Euclidean counterpart and existing embedding methods on the link prediction task, particularly at lower dimensionality.