One of the important assumptions of linear regression is that, there should be no heteroscedasticity of residuals. In simpler terms, this means that the variance of residuals should not increase with fitted values of response variable. In this post, I am going to explain why it is important to check for heteroscedasticity, how to detect it in your model? If is present, how to make amends to rectify the problem, with example R codes. This process is sometimes referred to as residual analysis.

This will be a journey into predicting whether or not observations, made by high powered telescopes on Earth and potentially deep space probes in the future, are pulsars. Before we jump into the machine learning model I have developed to help identify pulsars, let's talk a bit about what pulsars, or'pulsar stars', actually are since they aren't pulsating and actually aren't technically stars (anymore). Consider, for the sake of explanation, that stars have a life. If they are less massive, between 7 and 25 solar masses (7–25 times the mass of our sun) or maybe a bit larger if they are especially metal-rich, they then become neutron stars, a super-dense mass only around 10 kilometers in radius but so dense that a teaspoon full of their mass would be as heavy as Mt. Everest if placed on Earth.

Purpose: Coronavirus 2019 (COVID-19), which emerged in Wuhan, China and affected the whole world, has cost the lives of thousands of people. Manual diagnosis is inefficient due to the rapid spread of this virus. For this reason, automatic COVID-19 detection studies are carried out with the support of artificial intelligence algorithms. Methods: In this study, a deep learning model that detects COVID-19 cases with high performance is presented. The proposed method is defined as Convolutional Support Vector Machine (CSVM) and can automatically classify Computed Tomography (CT) images.

The consistency of a response to a given post at semantic-level and emotional-level is essential for a dialogue system to deliver human-like interactions. However, this challenge is not well addressed in the literature, since most of the approaches neglect the emotional information conveyed by a post while generating responses. This article addresses this problem by proposing a unifed end-to-end neural architecture, which is capable of simultaneously encoding the semantics and the emotions in a post and leverage target information for generating more intelligent responses with appropriately expressed emotions. Extensive experiments on real-world data demonstrate that the proposed method outperforms the state-of-the-art methods in terms of both content coherence and emotion appropriateness.

We study the problem of learning a robot policy to follow natural language instructions that can be easily extended to reason about new objects. We introduce a few-shot language-conditioned object grounding method trained from augmented reality data that uses exemplars to identify objects and align them to their mentions in instructions. We present a learned map representation that encodes object locations and their instructed use, and construct it from our few-shot grounding output. We integrate this mapping approach into an instruction-following policy, thereby allowing it to reason about previously unseen objects at test-time by simply adding exemplars. We evaluate on the task of learning to map raw observations and instructions to continuous control of a physical quadcopter. Our approach significantly outperforms the prior state of the art in the presence of new objects, even when the prior approach observes all objects during training.

In e-commerce portals, generating answers for product-related questions has become a crucial task. In this paper, we focus on the task of product-aware answer generation, which learns to generate an accurate and complete answer from large-scale unlabeled e-commerce reviews and product attributes. However, safe answer problems pose significant challenges to text generation tasks, and e-commerce question-answering task is no exception. To generate more meaningful answers, in this paper, we propose a novel generative neural model, called the Meaningful Product Answer Generator (MPAG), which alleviates the safe answer problem by taking product reviews, product attributes, and a prototype answer into consideration. Product reviews and product attributes are used to provide meaningful content, while the prototype answer can yield a more diverse answer pattern. To this end, we propose a novel answer generator with a review reasoning module and a prototype answer reader. Our key idea is to obtain the correct question-aware information from a large scale collection of reviews and learn how to write a coherent and meaningful answer from an existing prototype answer. To be more specific, we propose a read-and-write memory consisting of selective writing units to conduct reasoning among these reviews. We then employ a prototype reader consisting of comprehensive matching to extract the answer skeleton from the prototype answer. Finally, we propose an answer editor to generate the final answer by taking the question and the above parts as input. Conducted on a real-world dataset collected from an e-commerce platform, extensive experimental results show that our model achieves state-of-the-art performance in terms of both automatic metrics and human evaluations. Human evaluation also demonstrates that our model can consistently generate specific and proper answers.

Modern neural networks have the capacity to overfit noisy labels frequently found in real-world datasets. Although great progress has been made, existing techniques are limited in providing theoretical guarantees for the performance of the neural networks trained with noisy labels. Here we propose a novel approach with strong theoretical guarantees for robust training of deep networks trained with noisy labels. The key idea behind our method is to select weighted subsets (coresets) of clean data points that provide an approximately low-rank Jacobian matrix. We then prove that gradient descent applied to the subsets do not overfit the noisy labels. Our extensive experiments corroborate our theory and demonstrate that deep networks trained on our subsets achieve a significantly superior performance compared to state-of-the art, e.g., 6% increase in accuracy on CIFAR-10 with 80% noisy labels, and 7% increase in accuracy on mini Webvision.

We adapt previous research on topological unsupervised learning to develop a unified functorial perspective on manifold learning and clustering. We first introduce overlapping hierachical clustering algorithms as functors and demonstrate that the maximal and single linkage clustering algorithms factor through an adaptation of the singular set functor. Next, we characterize manifold learning algorithms as functors that map uber-metric spaces to optimization objectives and factor through hierachical clustering functors. We use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their invariants. We express several state of the art manifold learning algorithms as functors at different levels of this hierarchy, including Laplacian Eigenmaps, Metric Multidimensional Scaling, and UMAP. Finally, we experimentally demonstrate that this perspective enables us to derive and analyze novel manifold learning algorithms.

Let's approach this problem of feature selection using Chi-Square a question and answer style. If you are a video guy, you may check out our youtube lecture on the same. Question 1: What is a feature? For any ML or DL problem, the data is arranged in rows and columns. Let's take the example of a titanic shipwreck problem. Question 2: What are the different types of features?