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Bayesian Methods for Hackers

Bayesian Methods for Hackers
An intro to Bayesian methods and probabilistic programming from a computation/understanding-first, mathematics-second point of view. Prologue The Bayesian method is the natural approach to inference, yet it is hidden from readers behind chapters of slow, mathematical analysis. The typical text on Bayesian inference involves two to three chapters on probability theory, then enters what Bayesian inference is. Unfortunately, due to mathematical intractability of most Bayesian models, the reader is only shown simple, artificial examples. This can leave the user with a so-what feeling about Bayesian inference. After some recent success of Bayesian methods in machine-learning competitions, I decided to investigate the subject again. If Bayesian inference is the destination, then mathematical analysis is a particular path towards it. Bayesian Methods for Hackers is designed as a introduction to Bayesian inference from a computational/understanding-first, and mathematics-second, point of view. Related:  Data science tutorialsMachine learning

Implementation of k-means Clustering - Edureka In this blog, you will understand what is K-means clustering and how it can be implemented on the criminal data collected in various US states. The data contains crimes committed like: assault, murder, and rape in arrests per 100,000 residents in each of the 50 US states in 1973. Along with analyzing the data you will also learn about: Finding the optimal number of clusters.Minimizing distortionCreating and analyzing the elbow curve.Understanding the mechanism of k-means algorithm. Let us start with the analysis. The data looks as: Click on the image to download this dataset Need this dataset? First let’s prepare the data for the analysis. > crime0 <- na.omit(USArrests) > crime <- data.matrix (crime0) > str(crime) num [1:50, 1:4] 13.2 10 8.1 8.8 9 7.9 3.3 5.9 15.4 17.4 ... - attr(*, "dimnames")=List of 2 ..$ : chr [1:50] "Alabama" "Alaska" "Arizona" "Arkansas" ... ..$ : chr [1:4] "Murder" "Assault" "UrbanPop" "Rape" Let us take the number of clusters to be 5. Analyzing the Clustering :

Neural networks and deep learning The human visual system is one of the wonders of the world. Consider the following sequence of handwritten digits: Most people effortlessly recognize those digits as 504192. That ease is deceptive. The difficulty of visual pattern recognition becomes apparent if you attempt to write a computer program to recognize digits like those above. Neural networks approach the problem in a different way. and then develop a system which can learn from those training examples. In this chapter we'll write a computer program implementing a neural network that learns to recognize handwritten digits. We're focusing on handwriting recognition because it's an excellent prototype problem for learning about neural networks in general. Of course, if the point of the chapter was only to write a computer program to recognize handwritten digits, then the chapter would be much shorter! Perceptrons What is a neural network? So how do perceptrons work? That's the basic mathematical model. Is the weather good?

Eigenvectors and eigenvalues explained visually Explained Visually By Victor Powell and Lewis Lehe Eigenvalues/vectors are instrumental to understanding electrical circuits, mechanical systems, ecology and even Google's PageRank algorithm. To begin, let $v$ be a vector (shown as a point) and $A$ be a matrix with columns $a_1$ and $a_2$ (shown as arrows). If you can draw a line through the three points $(0,0)$, $v$ and $Av$, then $Av$ is just $v$ multiplied by a number $\lambda$; that is, $Av = \lambda v$. Below, change the columns of $A$ and drag $v$ to be an eigenvector. What are eigenvalues/vectors good for? If you keep multiplying $v$ by $A$, you get a sequence ${ v, Av, A^2v,}$ etc. Let's explore some applications and properties of these sequences. Fibonacci Sequence Suppose you have some amoebas in a petri dish. which we can rewrite in matrix form like Below, press "Forward" to step ahead a minute. 1 child + 0 adults = 1 As you can see, the system goes toward the grey line, which is an eigenspace with $\lambda = (1+\sqrt 5)/2 > 1$.

Introduction to Color Scheme Extraction - Algorithmia As an artist, inspiration can come from anywhere: a particular texture, a design, or even a color scheme. Instead of spending hours painstakingly extracting the hex codes from all of the important sections of an image, what if there was a way to automatically extract the most important parts of an image? Color Scheme extraction is able to find the most relevant colors in seconds. What Is Color Scheme Extraction? Color Scheme extraction is an open source algorithm using the scikit-learn framework that extracts color schemes from images. Pixel clusters are generated with varying initial conditions and scored on overall accuracy until the iteration limit is reached. Why You Need Color Scheme Extraction Complex images with gradients just have too many colors to be able to easily extract a representative palette. How Do I Use Color Scheme Extraction? Sample Input: Sample Output: That’s it! What if you want to extract even more information from images or even generate your own filters?

Блог / Хабрацентр им. moat 15 марта 2015 в 18:58 Представляю вашему вниманию очередной выпуск обзора наиболее интересных материалов, посвященных теме анализа данных и машинного обучения. 16,4k 138 @moat 10 марта 2015 в 11:52 7,5k 76 @moat 1 марта 2015 в 19:07 8,5k 83 @moat 22 февраля 2015 в 16:51 8,8k 90 @moat 15 февраля 2015 в 15:03 9,2k 96 @moat 9 февраля 2015 в 16:53 6,9k 103 @moat 1 февраля 2015 в 15:55 9,7k 114 @moat 25 января 2015 в 19:14 9,6k 108 @moat 18 января 2015 в 18:02 11,4k 125 @moat 11 января 2015 в 19:54 7,6k 97 @moat Yudkowsky - Bayes' Theorem An Intuitive Explanation of Bayes' Theorem Bayes' Theorem for the curious and bewildered; an excruciatingly gentle introduction. Your friends and colleagues are talking about something called "Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning. It's this equation. So you came here. Why does a mathematical concept generate this strange enthusiasm in its students? Soon you will know. While there are a few existing online explanations of Bayes' Theorem, my experience with trying to introduce people to Bayesian reasoning is that the existing online explanations are too abstract. Or so they claim. And let's begin. Here's a story problem about a situation that doctors often encounter: 1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. What do you think the answer is? Group 1: 100 women with breast cancer.

Rotate Images in Python Using a Horizon Detection Algorithm - Algorithmia When we look at an image, it’s fairly easy to detect the horizon line. For computers, this task is somewhat more difficult: they need to understand the basic structure of the image, locate edges which might indicate a horizon, and pare out the edges which do not matter. Fortunately, Algorithmia boils this all down to a single API call: just send your image to deep horizon, an algorithm for horizon detection, and it tells you where the horizon line is. Let’s see how we can use this tool, in combination with Pillow (a fork of the Python Image Library), to automatically recompose any image so it’s level. Step 1: Install the Algorithmia Client While this demo is written using our Python client, our services are equally easy to use in a variety of other programming languages, or even via cURL. pip install algorithmia You’ll also need a free Algorithmia account, which includes 5,000 free credits a month – enough to level thousands of images. To get started, simply sign up, then grab your API key.

Reflecting back on one year of Kaggle contests | MLWave It’s been a year since I joined Kaggle for my first competition. Back then I didn’t know what an Area Under the Curve was. How did I manage to predict my way to Kaggle Master? Early start Toying with datasets and tools I was already downloading datasets from Kaggle purely for my own entertainment and study before I started competing. The dataset for the “ – Employee Access Challenge” was one of the first datasets that caught my eyes. Or maybe not; such a simple (linear) algorithm really has no right being so good for a problem like this… The Kaggle forums It was Miroslaw Horbal who really got me hooked on the Kaggle forums with his post: How to achieve 0.90AUC with Logistic Regression. Competing on Kaggle StumbleUpon Evergreen Classification Challenge This was my first contest. That all changed when Abhishek Thakur shared his beat the benchmark post on the forums. After a few weeks I found a way to improve the score by using WordnetLemmatizer from NLTK. I finished top 25%. Resources

Bayes’ Theorem, Predictions and Confidence Intervals / Algorithms There are plenty of articles on this subject, but they do not review real-life problems. I am going to try to fix this. We use Bayes’ Theorem (a.k.a. Bayes’ law or Bayes’ rule) to filter spam in recommendation services and for ratings system. A great number of algorithms of fuzzy searches would be impossible without it. Besides, the theorem is the cause of holy wars between mathematicians. Introduction Let’s start from the very beginning. Let’s introduce the following notions: P(A) is the probability of A event occurrence.P(AB) is the probability of both events occurrence. Let’s think. It’s so simple that 300 years ago a priest derived it. Direct and Inverse Problems We can describe a direct problem the following way: find the probability of one of effects by a reason. But the problem is that we do not know the probability of some event in minority of cases only. In practice, the inverse task is more important. We have to use some function. Binomial Distribution P([s,d]|p=x). Holy War

Introducing Cloud Hosted Deep Learning Models Introducing Cloud Hosted Deep Learning Models At Algorithmia, we believe in democratizing access to state-of-the-art algorithmic intelligence. That’s why we’re introducing a solution for hosting and distributing trained deep learning models on Algorithmia using GPUs in the cloud. Today, researchers and developers can train their neural nets locally, and deploy them to Algorithmia’s scalable, cloud infrastructure, where they become smart API endpoints for other developers to use. We’re excited to announce initial native support for the Caffe, Theano, and TensorFlow frameworks, and have added 16 open source deep learning models that run as microservices to start. Support for Torch and MxNet are coming soon. Grab out developer guides for Caffe, TensorFlow, and Theano here. Plus, we’ve created two demos to showcase how easy it is to build applications off of hosted models: We believe algorithms and models should be implemented once, reusable by developers anywhere, in any language.

III Корреляционный анализ. 1. Понятие корреляции. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.ЛИНЕЙНАЯ КОРРЕЛЯЦИЯ (пояснения и иллюстрации) Несмотря на наличие ссылок по тексту, автор все же рекомендует прочесть раздел целиком - для более последовательного понимания материала. 1. 2. 3. Рисунок 14. 4. 5. По форме – зависимость может быть линейной и нелинейной. Рисунок 15. По направлению – усилению одного признака соответствует усиление другого при прямом направлении корреляции и ослабление - при обратном. По силе – сила связи не зависит от направления и определяется абсолютной величиной коэффициента корреляции r. 6. А) общая: Б) частная: Первая из классификаций ориентирована только на величину коэффициента корреляции, а вторая определяет, какого уровня значимости достигает данная величина коэффициента корреляции при данном объеме выборки. Пример: "отношение числа новорожденных мальчиков к числу новорожденных девочек" Рассмотрим следующий пример, заимствованный из Nisbett, et al., 1987. 7. 8. 9. 10. 11. Где:

Differential Equations Explained $\cos$PLAY You're probably used to equations like $$(t-.5)(t-1)= 0,$$ where 'solving' means finding an unknown number. A differential equation (DE), by contrast, is a fact about the derivative of an unknown function, and 'solving' one means finding a function that fits. To visualize derivatives, we can draw a right triangle whose hypoteneuse is tangent to a function. If the triangle's width is $1$, then its height is the derivative. With that one weird trick, the plots to the right show how the derivative of $\sin(t)$ is $\cos(t)$. That's a pretty basic DE, though. Consider a cart rolling to a stop. The solution is a function $v(t)$ giving velocity at time $t$. It turns out the exponential function, $e^{-kt}$, has the properties $$ \begin{align} \frac{d}{dt}e^{-kt}=-ke^{-kt} && e^{-k\cdot 0}=1. To make the solution more intuitive, here you'll solve the cart's DE manually by picking a series of $\left( t, v \right)$ points. The first cart below obeys the $v(t)$ function you designed.