Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlike the classical higher-order singular value decomposition which unfolds a tensor along a single mode, we consider unfoldings along two modes and use rank-1 constraints to characterize the underlying components. This tensor decomposition method provably handles a greater level of noise compared to previous methods and achieves a high estimation accuracy. Numerical results demonstrate that our algorithm is robust to various noise distributions and that it performs especially favorably as the order increases.

This paper describes a new neuroimaging analysis toolbox that allows for the modeling of nonlinear effects at the voxel level, overcoming limitations of methods based on linear models like the GLM. We illustrate its features using a relevant example in which distinct nonlinear trajectories of Alzheimer's disease related brain atrophy patterns were found across the full biological spectrum of the disease. The open-source toolbox is available in GitHub: https://github.com/

In our world, many of the commonly encountered problems are classification problems. We are often confused between definite values or rigid choices of things. In this article, we will discuss about an algorithm used to solve simple classification problems effectively using Machine Learning. Also, we will analyze a hypothetical Binary Class problem involving Grad-School outcomes based on the Entrance Exam Marks and the Undergrad Marks. Supervised Learning is a machine learning technique in which we associate our inputs with our targets in the given dataset. We already have a definite intuition regarding our final output.

Which authors of this paper are endorsers? Disable MathJax (What is MathJax?)

Data science and machine learning have long been interests of mine, but now that I'm working on Fuzzy.ai and trying to make AI and machine learning accessible to all developers, I need to keep on top of all the news in both fields. My preferred way to do this is through listening to podcasts. I've listened to a bunch of machine learning and data science podcasts in the last few months, so I thought I'd share my favorites: Every other week, they release a 10–15 minute episode where hosts, Kyle and Linda Polich give a short primer on topics like k-means clustering, natural language processing and decision tree learning, often using analogies related to their pet parrot, Yoshi. This is the only place where you'll learn about k-means clustering via placement of parrot droppings. Hosted by Katie Malone and Ben Jaffe of online education startup Udacity, this weekly podcast covers diverse topics in data science and machine learning: teaching specific concepts like Hidden Markov Models and how they apply to real-world problems and datasets.

While there's not necessarily a "correct" answer here, it's most likely you split the bugs into four clusters. That wasn't too bad, was it? You could probably do the same with twice as many bugs, right? If you had a bit of time to spare -- or a passion for entomology -- you could probably even do the same with a hundred bugs. For a machine though, grouping ten objects into however many meaningful clusters is no small task, thanks to a mind-bending branch of maths called combinatorics, which tells us that are 115,975 different possible ways you could have grouped those ten insects together. Had there been twenty bugs, there would have been over fifty trillion possible ways of clustering them. With a hundred bugs -- there'd be many times more solutions than there are particles in the known universe. In fact, there are more than four million billion googol solutions (what's a googol?).

In the customer management lifecycle, customer churn refers to a decision made by the customer about ending the business relationship. It is also referred as loss of clients or customers. Customer loyalty and customer churn always add up to 100%. If a firm has a 60% of loyalty rate, then their loss or churn rate of customers is 40%. As per 80/20 customer profitability rule, 20% of customers are generating 80% of revenue.

In this paper, we propose a simple variant of the original stochastic variance reduction gradient (SVRG), where hereafter we refer to as the variance reduced stochastic gradient descent (VR-SGD). Different from the choices of the snapshot point and starting point in SVRG and its proximal variant, Prox-SVRG, the two vectors of each epoch in VR-SGD are set to the average and last iterate of the previous epoch, respectively. This setting allows us to use much larger learning rates or step sizes than SVRG, e.g., 3/(7L) for VR-SGD vs 1/(10L) for SVRG, and also makes our convergence analysis more challenging. In fact, a larger learning rate enjoyed by VR-SGD means that the variance of its stochastic gradient estimator asymptotically approaches zero more rapidly. Unlike common stochastic methods such as SVRG and proximal stochastic methods such as Prox-SVRG, we design two different update rules for smooth and non-smooth objective functions, respectively. In other words, VR-SGD can tackle non-smooth and/or non-strongly convex problems directly without using any reduction techniques such as quadratic regularizers. Moreover, we analyze the convergence properties of VR-SGD for strongly convex problems, which show that VR-SGD attains a linear convergence rate. We also provide the convergence guarantees of VR-SGD for non-strongly convex problems. Experimental results show that the performance of VR-SGD is significantly better than its counterparts, SVRG and Prox-SVRG, and it is also much better than the best known stochastic method, Katyusha.

We introduce a novel Bayesian hybrid matrix factorisation model (HMF) for data integration, based on combining multiple matrix factorisation methods, that can be used for in- and out-of-matrix prediction of missing values. The model is very general and can be used to integrate many datasets across different entity types, including repeated experiments, similarity matrices, and very sparse datasets. We apply our method on two biological applications, and extensively compare it to state-of-the-art machine learning and matrix factorisation models. For in-matrix predictions on drug sensitivity datasets we obtain consistently better performances than existing methods. This is especially the case when we increase the sparsity of the datasets. Furthermore, we perform out-of-matrix predictions on methylation and gene expression datasets, and obtain the best results on two of the three datasets, especially when the predictivity of datasets is high.

Associating image regions with text queries has been recently explored as a new way to bridge visual and linguistic representations. A few pioneering approaches have been proposed based on recurrent neural language models trained generatively (e.g., generating captions), but achieving somewhat limited localization accuracy. To better address natural-language-based visual entity localization, we propose a discriminative approach. We formulate a discriminative bimodal neural network (DBNet), which can be trained by a classifier with extensive use of negative samples. Our training objective encourages better localization on single images, incorporates text phrases in a broad range, and properly pairs image regions with text phrases into positive and negative examples. Experiments on the Visual Genome dataset demonstrate the proposed DBNet significantly outperforms previous state-of-the-art methods both for localization on single images and for detection on multiple images. We we also establish an evaluation protocol for natural-language visual detection.