Nonnegative matrix factorization (NMF) is a widely used linear dimensionality reduction technique for nonnegative data. NMF requires that each data point is approximated by a convex combination of basis elements. Archetypal analysis (AA), also referred to as convex NMF, is a well-known NMF variant imposing that the basis elements are themselves convex combinations of the data points. AA has the advantage to be more interpretable than NMF because the basis elements are directly constructed from the data points. However, it usually suffers from a high data fitting error because the basis elements are constrained to be contained in the convex cone of the data points. In this letter, we introduce near-convex archetypal analysis (NCAA) which combines the advantages of both AA and NMF. As for AA, the basis vectors are required to be linear combinations of the data points and hence are easily interpretable. As for NMF, the additional flexibility in choosing the basis elements allows NCAA to have a low data fitting error. We show that NCAA compares favorably with a state-of-the-art minimum-volume NMF method on synthetic datasets and on a real-world hyperspectral image.

On top of recommending the excellent autobiography of Stanislaw Ulam, this post is about using the software Stan, but not directly to perform inference, instead to obtain R functions to evaluate a target's probability density function and its gradient. With which, one can implement custom methods, while still benefiting from the great work of the Stan team on the "modeling language" side. As a proof of concept I have implemented a plain Hamiltonian Monte Carlo sampler for a random effect logistic regression model (taken from a course on Multilevel Models by Germán Rodríguez), a coupling of that HMC algorithm (as in "Unbiased Hamiltonian Monte Carlo with couplings", see also this very recent article on the topic of coupling HMC), and then upper bounds on the total variation distance between the chain and its limiting distribution, as in "Estimating Convergence of Markov chains with L-Lag Couplings". Basically the R script starts like a standard script that would use rstan for inference; it runs the default algorithm of Stan for a little while, then extracts some info from the "stanfit" object. With these, a pure R implementation of TV upper bounds for a naive HMC algorithm follows, that relies on functions called "stan_logtarget" and "stan_gradlogtarget" to evaluate the target log-pdf and its gradient.

From the n independent variables of the dataset, LDA extracts p n new independent variables that separate the most the classes of the dependent variable. The dataset, in this case, is the same dataset as the PCA technique. The steps are also almost similar. The second step is to construct the LDA object and etc. It is required to create an LDA object by using a linear discriminant analysis class from the sklearn library.

Modern artificial intelligence lacks a strong theoretical basis, and so it's often a shrug of the shoulders why it works at all (or, oftentimes, doesn't entirely work). One of the deepest mysteries of deep learning is one of its most brilliant successes, what's known as stochastic gradient descent. Stochasticity, the process of randomly picking out examples of data, has yielded breakthroughs in image recognition and other deep learning tasks. And now, one computer chip company thinks they may have a kind of machine for stochasticity, a chip whose power comes from randomness. It might not lead to a theory of why machine learning works, but it might lead to knew breakthroughs in what stochasticity can achieve.

Increasingly, the data that is relevant for companies' machine learning efforts will be not just ... [ ] some data, but all of it; anything less risks missing what could conceivably be the critical insight down the road, the answer to questions as yet unasked. Chief information officers of companies have a strange predicament in an age of AI: They are meant to solve problems for companies by marshaling the relevant data on customers and transactions, but the data itself is going to raise new, unexpected questions. Increasingly, the data that is relevant for companies' machine learning efforts will be not just some data, but all of it; anything less risks missing what could conceivably be the critical insight down the road, the answer to questions as yet unasked. Until recently, the era of "big data," as it's called, has been about providing only the requisite information to answer some straightforward question, where the "known unknowns" are all that matters. For example, if you're a retailer, you might want to know how many of your customers would be likely to return items they've bought based on patterns of purchases.

In this article, we will study the various types of machine learning algorithms and their use-cases. We will study how Baidu is using supervised learning-based facial recognition for intelligent airport check-in and how Google is making use of Reinforcement Learning to develop an intelligent platform that would answer your queries. Machine Learning is a broad field, but it is classified into three classes of supervised, unsupervised and reinforcement learning. All these three paradigms are used everywhere to power intelligent applications. We will look at the important use cases of these paradigms and how they are revolutionizing our world today.

A member of the generalized linear model (GLM) family and similar to linear regression in many ways, logistic regression (despite the confusing name) is used for classification problems with two possible outcomes. Logistic regression is handy for classification problems since it fits an S shaped logistic (or Sigmoid) function to the data, squishing the linear equation to an output range of 0–1. This convenient range allows logistic regression to model the probabilities of a data point belonging to a particular class, typically with the decision point at the probability of .5. So, what does that look like in math? How does the sigmoid function squish the linear equation?

Till now, all algorithms being introduced are either value function or Q function based gradient algorithm, that is we assume there exists a true value V(or Q) for different state S(or [S, A]), and to approach the true value we use gradient method that comes with either V or Q in the formula, and and the end of the learning process, a policy π(A S) is generated by choosing the most rewarding action at each state based on V or Q function estimation. However, policy gradient method proposes a total different view on reinforcement learning problems, instead of learning a value function, one can directly learn or update a policy. Remember in previous posts, the policy being used in the learning process is always ϵ-greedy, which means the agent will take random action will a certain probability and take greedy action in the rest. However, in gradient policy method, the problem is formulated as, P(A S, θ) π(A S, θ), which is saying, for each state, the policy gives a probability of each action possible taken from that state, and in order to optimise the policy, it is parameterised with θ (similar to weight parameter w in value function we introduced before). And because of J is a representation of policy π, we know that the update of θ will include the current policy, and after a series of deduction(for details, please refer to Sutton's book, chapter 13), we get the update process: G is still the cumulative discounted reward, and the parameter θ will be updated with current derivative of policy.

In the following, we will show that not only is there no need to choose between power and explainability, but that more powerful models are even more explainable than the shallower ones. By way of illustration, we will be using one of the most well-known datasets: the iconic Titanic dataset. We have a bunch of variables about Titanic passengers, and we want to predict how likely each passenger is to survive. For what concerns classification problems, Logistic Regression is often taken as the baseline. After having one-hot encoded the qualitative features (Ticket class, Passenger sex and Port of embarkation), we fit a plain Logistic Regression on the training data.

Blog: medium @newfrontcreative Biography Scott Haines is a Principal Software Engineer on the Voice Insights team at Twilio. His focus has been on the architecture and development of a real-time (sub 250ms), highly available, trustworthy analytics system. His team is providing near real-time analytics that processes / aggregates and analyzes multiple terabytes of global sensor data daily. Scott helped drive Apache Spark adoption at Twilio and actively teaches and consulting teams internally. Scott's past experience was at Yahoo! where he built a real-time recommendation engine and targeted ranking / ratings analytics which helped serve personalized page content for millions of customers of Yahoo Games.