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 Statistical Learning


Vaimal - Machine Learning Add-In - Vortarus Technologies LLC

#artificialintelligence

Vaimal is a machine learning add-in that allows you to train and deploy machine learning algorithms without programming. You can make predictions on new data using models that are trained on historical data. Vaimal allows you to create decision trees, support vector machines and neural networks all within Excel . It also includes more powerful ensemble methods to combine models for even better predictive performance. The easy to use interface allows you to focus on your data without worrying about learning mundane programming tasks required with common machine learning platforms.


Dimensionality Reduction For Dummies -- Part 1: Intuition

#artificialintelligence

We need to see in order to believe. When you have a dataset with more than three dimensions, it becomes impossible to see what's going on with our eyes. But who said that these extra dimensions are really necessary? Isn't there a way to somehow reduce it to one, two, or three humanly dimensions? It turns out there is.


Feature Selection and Comparison of Machine Learning Algorithms in Classification of Grazing and Rumination Behaviour in Sheep

#artificialintelligence

Grazing and ruminating are the most important behaviours for ruminants, as they spend most of their daily time budget performing these. Continuous surveillance of eating behaviour is an important means for monitoring ruminant health, productivity and welfare. However, surveillance performed by human operators is prone to human variance, time-consuming and costly, especially on animals kept at pasture or free-ranging. The use of sensors to automatically acquire data, and software to classify and identify behaviours, offers significant potential in addressing such issues. In this work, data collected from sheep by means of an accelerometer/gyroscope sensor attached to the ear and collar, sampled at 16 Hz, were used to develop classifiers for grazing and ruminating behaviour using various machine learning algorithms: random forest (RF), support vector machine (SVM), k nearest neighbour (kNN) and adaptive boosting (Adaboost).


A Model Parallel Proximal Stochastic Gradient Algorithm for Partially Asynchronous Systems

arXiv.org Machine Learning

Large models are prevalent in modern machine learning scenarios, including deep learning, recommender systems, etc., which can have millions or even billions of parameters. Parallel algorithms have become an essential solution technique to many large-scale machine learning jobs. In this paper, we propose a model parallel proximal stochastic gradient algorithm, AsyB-ProxSGD, to deal with large models using model parallel blockwise updates while in the meantime handling a large amount of training data using proximal stochastic gradient descent (ProxSGD). In our algorithm, worker nodes communicate with the parameter servers asynchronously, and each worker performs proximal stochastic gradient for only one block of model parameters during each iteration. Our proposed algorithm generalizes ProxSGD to the asynchronous and model parallel setting. We prove that AsyB-ProxSGD achieves a convergence rate of $O(1/\sqrt{K})$ to stationary points for nonconvex problems under \emph{constant} minibatch sizes, where $K$ is the total number of block updates. This rate matches the best-known rates of convergence for a wide range of gradient-like algorithms. Furthermore, we show that when the number of workers is bounded by $O(K^{1/4})$, we can expect AsyB-ProxSGD to achieve linear speedup as the number of workers increases. We implement the proposed algorithm on MXNet and demonstrate its convergence behavior and near-linear speedup on a real-world dataset involving both a large model size and large amounts of data.


Learning Models with Uniform Performance via Distributionally Robust Optimization

arXiv.org Machine Learning

In many applications of statistics and machine learning, we wish to learn models that achieve uniformly good performance over almost all input values. This is important for safety-and fairnesscritical systems such as medical diagnosis, autonomous vehicles, criminal justice and credit evaluations, where poor performance on the tails of the inputs leads to high-cost system failures. Methods that optimize average performance, however, often produce models that suffer low performance on the "hard" instances of the population. For example, standard regressors obtained from maximum likelihood estimation can lose their predictive power on certain regions of covariates [57], so that high average performance comes at the expense of low performance on minority subpopulations. In this work, we propose and study a procedure that explicitly optimizes performance on tail inputs that suffer high loss. Modern datasets incorporate heterogeneous (but latent) subpopulations, and a natural goal is to perform well across all of these [57, 65, 21]. While many statistical models show strong average performance, their performance often deteriorates on minority groups underrepresented in the dataset. For example, speech recognition systems are inaccurate for people with minority accents [4]. In numerous other applications--such as facial recognition, automatic video captioning, language identification, academic recommender systems--performance varies significantly over different demographic groupings, such as race, gender, or age [38, 42, 18, 68, 76].


Condition Number Analysis of Logistic Regression, and its Implications for Standard First-Order Solution Methods

arXiv.org Machine Learning

Logistic regression is one of the most popular methods in binary classification, wherein estimation of model parameters is carried out by solving the maximum likelihood (ML) optimization problem, and the ML estimator is defined to be the optimal solution of this problem. It is well known that the ML estimator exists when the data is non-separable, but fails to exist when the data is separable. First-order methods are the algorithms of choice for solving large-scale instances of the logistic regression problem. In this paper, we introduce a pair of condition numbers that measure the degree of non-separability or separability of a given dataset in the setting of binary classification, and we study how these condition numbers relate to and inform the properties and the convergence guarantees of first-order methods. When the training data is non-separable, we show that the degree of non-separability naturally enters the analysis and informs the properties and convergence guarantees of two standard first-order methods: steepest descent (for any given norm) and stochastic gradient descent. Expanding on the work of Bach, we also show how the degree of non-separability enters into the analysis of linear convergence of steepest descent (without needing strong convexity), as well as the adaptive convergence of stochastic gradient descent. When the training data is separable, first-order methods rather curiously have good empirical success, which is not well understood in theory. In the case of separable data, we demonstrate how the degree of separability enters into the analysis of $\ell_2$ steepest descent and stochastic gradient descent for delivering approximate-maximum-margin solutions with associated computational guarantees as well. This suggests that first-order methods can lead to statistically meaningful solutions in the separable case, even though the ML solution does not exist.


CNN inference acceleration using dictionary of centroids

arXiv.org Machine Learning

It is well known that multiplication operations in convolutional layers of common CNNs consume a lot of time during inference stage. In this article we present a flexible method to decrease both computational complexity of convolutional layers in inference as well as amount of space to store them. The method is based on centroid filter quantization and outperforms approaches based on tensor decomposition by a large margin. We performed comparative analysis of the proposed method and series of CP tensor decomposition on ImageNet benchmark and found that our method provide almost 2.9 times better computational gain. Despite the simplicity of our method it cannot be applied directly in inference stage in modern frameworks, but could be useful for cases calculation flow could be changed, e.g. for CNN-chip designers.


A Modern Take on the Bias-Variance Tradeoff in Neural Networks

arXiv.org Machine Learning

We revisit the bias-variance tradeoff for neural networks in light of modern empirical findings. The traditional bias-variance tradeoff in machine learning suggests that as model complexity grows, variance increases. Classical bounds in statistical learning theory point to the number of parameters in a model as a measure of model complexity, which means the tradeoff would indicate that variance increases with the size of neural networks. However, we empirically find that variance due to training set sampling is roughly constant (with both width and depth) in practice. Variance caused by the non-convexity of the loss landscape is different. We find that it decreases with width and increases with depth, in our setting. We provide theoretical analysis, in a simplified setting inspired by linear models, that is consistent with our empirical findings for width. We view bias-variance as a useful lens to study generalization through and encourage further theoretical explanation from this perspective. The traditional view in machine learning is that increasingly complex models achieve lower bias at the expense of higher variance. This balance between underfitting (high bias) and overfitting (high variance) is commonly known as the bias-variance tradeoff (Figure 1). In their landmark work that initially highlighted this bias-variance dilemma in machine learning, Geman et al. (1992) suggest that larger neural networks suffer from higher variance.


Nonparametric Bayesian Lomax delegate racing for survival analysis with competing risks

arXiv.org Machine Learning

We propose Lomax delegate racing (LDR) to explicitly model the mechanism of survival under competing risks and to interpret how the covariates accelerate or decelerate the time to event. LDR explains non-monotonic covariate effects by racing a potentially infinite number of sub-risks, and consequently relaxes the ubiquitous proportional-hazards assumption which may be too restrictive. Moreover, LDR is naturally able to model not only censoring, but also missing event times or event types. For inference, we develop a Gibbs sampler under data augmentation for moderately sized data, along with a stochastic gradient descent maximum a posteriori inference algorithm for big data applications. Illustrative experiments are provided on both synthetic and real datasets, and comparison with various benchmark algorithms for survival analysis with competing risks demonstrates distinguished performance of LDR.


Bayesian Distance Clustering

arXiv.org Machine Learning

Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density. Leveraging on properties of pairwise differences between data points, we propose a class of Bayesian distance clustering methods, which rely on modeling the likelihood of the pairwise distances in place of the original data. Although some information in the data is discarded, we gain substantial robustness to modeling assumptions. The proposed approach represents an appealing middle ground between distance- and model-based clustering, drawing advantages from each of these canonical approaches. We illustrate dramatic gains in the ability to infer clusters that are not well represented by the usual choices of kernel. A simulation study is included to assess performance relative to competitors, and we apply the approach to clustering of brain genome expression data. Keywords: Distance-based clustering; Mixture model; Model-based clustering; Model misspecification; Pairwise distance matrix; Partial likelihood; Robustness.