Software development begins as a quest for capability, doing what could not be done before. Once that what is achieved, the engineer is left with the how. In enterprise software, the most frequently asked questions are, "How fast?" and more importantly, "How reliable?" Questions about software performance cannot be answered, or even appropriately articulated, without statistics. Yet most developers can't tell you much about statistics. Much like math, statistics simply don't come up for typical projects. Between coding the new and maintaining the old, who has the time? Engineers must make the time. I understand fifteen minutes can seem like a big commitment these days, so maybe bookmark it. Insistent TLDR seekers can head for our instrumentation section or straight to the summary. For the dedicated few, class is in session.

Databases in domains such as healthcare are routinely released to the public in aggregated form. Unfortunately, naïve modeling with aggregated data may significantly diminish the accuracy of inferences at the individual level. This paper addresses the scenario where features are provided at the individual level, but the target variables are only available as histogram aggregates or order statistics. We consider a limiting case of generalized linear modeling when the target variables are only known up to permutation, and explore how this relates to permutation testing; a standard technique for assessing statistical dependency. Based on this relationship, we propose a simple algorithm to estimate the model parameters and individual level inferences via alternating imputation and standard generalized linear model fitting. Our results suggest the effectiveness of the proposed approach when, in the original data, permutation testing accurately ascertains the veracity of the linear relationship. The framework is extended to general histogram data with larger bins - with order statistics such as the median as a limiting case. Our experimental results on simulated data and aggregated healthcare data suggest a diminishing returns property with respect to the granularity of the histogram - when a linear relationship holds in the original data, the targets can be predicted accurately given relatively coarse histograms.

Learning the true ordering between objects by aggregating a set of expert opinion rank order lists is an important and ubiquitous problem in many applications ranging from social choice theory to natural language processing and search aggregation. We study the problem of unsupervised rank aggregation where no ground truth ordering information in available, neither about the true preference ordering between any set of objects nor about the quality of individual rank lists. Aggregating the often inconsistent and poor quality rank lists in such an unsupervised manner is a highly challenging problem, and standard consensus-based methods are often ill-defined, and difficult to solve. In this manuscript we propose a novel framework to bypass these issues by using object attributes to augment the standard rank aggregation framework. We design algorithms that learn joint models on both rank lists and object features to obtain an aggregated rank ordering that is more accurate and robust, and also helps weed out rank lists of dubious validity. We validate our techniques on synthetic datasets where our algorithm is able to estimate the true rank ordering even when the rank lists are corrupted. Experiments on three real datasets, MQ2008, MQ2008 and OHSUMED, show that using object features can result in significant improvement in performance over existing rank aggregation methods that do not use object information. Furthermore, when at least some of the rank lists are of high quality, our methods are able to effectively exploit their high expertise to output an aggregated rank ordering of great accuracy.

The k-Nearest Neighbors algorithm (or kNN for short) is an easy algorithm to understand and to implement, and a powerful tool to have at your disposal. In this tutorial you will implement the k-Nearest Neighbors algorithm from scratch in Python (2.7). The implementation will be specific for classification problems and will be demonstrated using the Iris flowers classification problem. This tutorial is for you if you are a Python programmer, or a programmer who can pick-up python quickly, and you are interested in how to implement the k-Nearest Neighbors algorithm from scratch. The model for kNN is the entire training dataset.

Machine learning is the process of building analytical models to automatically discover previously unknown patterns from data that indicate associations, sequences, anomalies (outliers), classifications, and clusters and segments. These patterns reveal hidden rules as to why an event happened--for example, rules that predict likely customer churn. The widely used Cross Industry Standard Process for Data Mining (CRISP-DM) methodology is used to develop predictive analytical models. CRISP-DM includes six phases: business understanding, data understanding, data preparation, model development using supervised and unsupervised learning, model evaluation and model deployment. The business understanding phase involves defining the business problem or use case, the business objectives and the business questions that need to be answered.

The amount of data produced every day grows tremendously in most real-life domains, including medical imaging, genomics, text categorisation, computational biology, and many others. Although it appears beneficial at the first glance (more data could mean more possibilities of extracting and revealing useful underlying knowledge), handling massively large datasets became a challenging issue and attracts research attention, especially in the era of big data. This big data revolution affected many research fields, including statistics, machine learning, parallel computing, and computer systems in general [1]. Storing and analysing the acquired historical information should allow predicting the label of an incoming (unseen) feature vector, containing some quantified features of a given data example. If the labels are categorical, then we are to tackle the classification task (it's regression otherwise).

Let's say that the average lifespan of a human being is L 70 years. The probability of dying this year, at any given age y, is p(y). Let's assume that the number of people that are y years old is M(y), and that p(y) is a monotonic decreasing function of age. If we have 7 billion human beings on Earth today, given these assumptions, how many will die this year? Now the question is: what is the lower and upper bounds for N (number of people who will die this year), regardless of the functions M() and p(), provided p() is monotonic decreasing, and that average age at death is L 70 years.

Azure Machine Learning Studio comes with a large number of machine learning algorithms that you can use to solve predictive analytics problems. The infographic below demonstrates how the four types of machine learning algorithms – regression, anomaly detection, clustering, and classification – can be used to answer your machine learning questions. The Microsoft Azure Machine Learning Algorithm Cheat Sheet helps you choose the right machine learning algorithm for your predictive analytics solutions from the Microsoft Azure Machine Learning library of algorithms. To download the cheat sheet and follow along with this article, go to Machine learning algorithm cheat sheet for Microsoft Azure Machine Learning Studio. This cheat sheet is perfect for students its aimed at someone with undergraduate-level machine learning, trying to choose an algorithm to start with in Azure Machine Learning Studio.

The Wisdom of Crowds is a phenomenon described in social science that suggests four criteria applicable to groups of people. It is claimed that, if these criteria are satisfied, then the aggregate decisions made by a group will often be better than those of its individual members. Inspired by this concept, we present a novel feedback framework for the cluster ensemble problem, which we call Wisdom of Crowds Cluster Ensemble (WOCCE). Although many conventional cluster ensemble methods focusing on diversity have recently been proposed, WOCCE analyzes the conditions necessary for a crowd to exhibit this collective wisdom. These include decentralization criteria for generating primary results, independence criteria for the base algorithms, and diversity criteria for the ensemble members. We suggest appropriate procedures for evaluating these measures, and propose a new measure to assess the diversity. We evaluate the performance of WOCCE against some other traditional base algorithms as well as state-of-the-art ensemble methods. The results demonstrate the efficiency of WOCCE's aggregate decision-making compared to other algorithms.

Gaussian process regression (GPR) is a non-parametric Bayesian technique for interpolating or fitting data. The main barrier to further uptake of this powerful tool rests in the computational costs associated with the matrices which arise when dealing with large data sets. Here, we derive some simple results which we have found useful for speeding up the learning stage in the GPR algorithm, and especially for performing Bayesian model comparison between different covariance functions. We apply our techniques to both synthetic and real data and quantify the speed-up relative to using nested sampling to numerically evaluate model evidences.