We propose a non-linear, Bayesian non-parametric latent variable model where the latent space is assumed to be sparse and infinite dimensional a priori using an Indian buffet process prior. A posteriori, the number of instantiated dimensions in the latent space is guaranteed to be finite. The purpose of placing the Indian buffet process on the latent variables is to: 1.) Automatically and probabilistically select the number of latent dimensions. 2.) Impose sparsity in the latent space, where the Indian buffet process will select which elements are exactly zero. Our proposed model allows for sparse, non-linear latent variable modeling where the number of latent dimensions is selected automatically. Inference is made tractable using the random Fourier approximation and we can easily implement posterior inference through Markov chain Monte Carlo sampling. This approach is amenable to many observation models beyond the Gaussian setting. We demonstrate the utility of our method on a variety of synthetic, biological and text datasets and show that we can obtain superior test set performance compared to previous latent variable models.

While mixture of linear regressions (MLR) is a well-studied topic, prior works usually do not analyze such models for prediction error. In fact, {\em prediction} and {\em loss} are not well-defined in the context of mixtures. In this paper, first we show that MLR can be used for prediction where instead of predicting a label, the model predicts a list of values (also known as {\em list-decoding}). The list size is equal to the number of components in the mixture, and the loss function is defined to be minimum among the losses resulted by all the component models. We show that with this definition, a solution of the empirical risk minimization (ERM) achieves small probability of prediction error. This begs for an algorithm to minimize the empirical risk for MLR, which is known to be computationally hard. Prior algorithmic works in MLR focus on the {\em realizable} setting, i.e., recovery of parameters when data is probabilistically generated by a mixed linear (noisy) model. In this paper we show that a version of the popular alternating minimization (AM) algorithm finds the best fit lines in a dataset even when a realizable model is not assumed, under some regularity conditions on the dataset and the initial points, and thereby provides a solution for the ERM. We further provide an algorithm that runs in polynomial time in the number of datapoints, and recovers a good approximation of the best fit lines. The two algorithms are experimentally compared.

Hope you all had a great Halloween weekend [ I dressed up as "Mother of Dragons" along with my cool " Game of thrones" techie friends];) #winteriscoming. Let's get back and learn some more data science and machine learning. I hope you all have already grasped the Python essentials, Statistics and Maths from day 1 -- day 8(links shared below), Pandas part 1 and part 2 on Day 9, Day 10, Numpy as Day 11, Data Preprocessing Part 1 as Day 12, Data Preprocessing part 2 as Day 13th, Hands on Regression Part 1 as Day 14th. In this post we will cover how we can implement Regression -- part 2 as Day 15. The Linear Regression method is basically a linear approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variables) as it just minimizes the least squares error: for one object target y x T * w, where w is model's weights.

Over the past a number of years, there was an elevated give attention to growing differential privateness (DP) machine studying (ML) algorithms. DP has been the idea of a number of sensible deployments in business -- and has even been employed by the U.S. Census -- as a result of it allows the understanding of system and algorithm privateness ensures. The underlying assumption of DP is that altering a single person's contribution to an algorithm mustn't considerably change its output distribution. In the usual supervised studying setting, a mannequin is educated to make a prediction of the label for every enter given a coaching set of instance pairs {[input1,label1], …, [inputn, labeln]}. Within the case of deep studying, earlier work launched a DP coaching framework, DP-SGD, that was built-in into TensorFlow and PyTorch.

Fragility hip fracture increases morbidity and mortality in older adult patients, especially within the first year. Identification of patients at high risk of death facilitates modification of associated perioperative factors that can reduce mortality. Various machine learning algorithms have been developed and are widely used in healthcare research, particularly for mortality prediction. This study aimed to develop and internally validate 7 machine learning models to predict 1-year mortality after fragility hip fracture. This retrospective study included patients with fragility hip fractures from a single center (Siriraj Hospital, Bangkok, Thailand) from July 2016 to October 2018. A total of 492 patients were enrolled. They were randomly categorized into a training group (344 cases, 70%) or a testing group (148 cases, 30%). Various machine learning techniques were used: the Gradient Boosting Classifier (GB), Random Forests Classifier (RF), Artificial Neural Network Classifier (ANN), Logistic Regression Classifier (LR), Naive Bayes Classifier (NB), Support Vector Machine Classifier (SVM), and K-Nearest Neighbors Classifier (KNN). All models were internally validated by evaluating their performance and the area under a receiver operating characteristic curve (AUC). For the testing dataset, the accuracies were GB model = 0.93, RF model = 0.95, ANN model = 0.94, LR model = 0.91, NB model = 0.89, SVM model = 0.90, and KNN model = 0.90. All models achieved high AUCs that ranged between 0.81 and 0.99. The RF model also provided a negative predictive value of 0.96, a positive predictive value of 0.93, a specificity of 0.99, and a sensitivity of 0.68. Our machine learning approach facilitated the successful development of an accurate model to predict 1-year mortality after fragility hip fracture. Several machine learning algorithms (eg, Gradient Boosting and Random Forest) had the potential to provide high predictive performance based on the clinical parameters of each patient. The web application is available at www.hipprediction.com . External validation in a larger group of patients or in different hospital settings is warranted to evaluate the clinical utility of this tool. Thai Clinical Trials Registry (22 February 2021; reg. no. TCTR20210222003 ).

This article was published as a part of the Data Science Blogathon. The variance is the difference between the model and the ground truth value, whereas the error is the outcome of sensitivity to tiny perturbations in the training set. Excessive bias might cause an algorithm to miss unique relationships between the intended outputs and the features (underfitting). There is a high variance in the algorithm that models random noise in the training data (overfitting). The bias-variance tradeoff is a characteristic of a model that states to lower the bias in estimated parameters, the variance of the parameter estimated across samples has increased.

Abstract: Two important nonparametric approaches to clustering emerged in the 1970's: clustering by level sets or cluster tree as proposed by Hartigan, and clustering by gradient lines or gradient flow as proposed by Fukunaga and Hosteler. In a recent paper, we argue the thesis that these two approaches are fundamentally the same by showing that the gradient flow provides a way to move along the cluster tree. In making a stronger case, we are confronted with the fact the cluster tree does not define a partition of the entire support of the underlying density, while the gradient flow does. Abstract: Mean shift is a simple interactive procedure that gradually shifts data points towards the mode which denotes the highest density of data points in the region. Mean shift algorithms have been effectively used for data denoising, mode seeking, and finding the number of clusters in a dataset in an automated fashion.

Noise is one of the primary quality-of-life issues in urban environments. In addition to annoyance, noise negatively impacts public health and educational performance. While low-cost sensors can be deployed to monitor ambient noise levels at high temporal resolutions, the amount of data they produce and the complexity of these data pose significant analytical challenges. One way to address these challenges is through machine listening techniques, which are used to extract features in attempts to classify the source of noise and understand temporal patterns of a city's noise situation. However, the overwhelming number of noise sources in the urban environment and the scarcity of labeled data makes it nearly impossible to create classification models with large enough vocabularies that capture the true dynamism of urban soundscapes In this paper, we first identify a set of requirements in the yet unexplored domain of urban soundscape exploration. To satisfy the requirements and tackle the identified challenges, we propose Urban Rhapsody, a framework that combines state-of-the-art audio representation, machine learning, and visual analytics to allow users to interactively create classification models, understand noise patterns of a city, and quickly retrieve and label audio excerpts in order to create a large high-precision annotated database of urban sound recordings. We demonstrate the tool's utility through case studies performed by domain experts using data generated over the five-year deployment of a one-of-a-kind sensor network in New York City.

Recommender Systems (RS) pervade many aspects of our everyday digital life. Proposed to work at scale, state-of-the-art RS allow the modeling of thousands of interactions and facilitate highly individualized recommendations. Conceptually, many RS can be viewed as instances of statistical regression models that incorporate complex feature effects and potentially non-Gaussian outcomes. Such structured regression models, including time-aware varying coefficients models, are, however, limited in their applicability to categorical effects and inclusion of a large number of interactions. Here, we propose Factorized Structured Regression (FaStR) for scalable varying coefficient models. FaStR overcomes limitations of general regression models for large-scale data by combining structured additive regression and factorization approaches in a neural network-based model implementation. This fusion provides a scalable framework for the estimation of statistical models in previously infeasible data settings. Empirical results confirm that the estimation of varying coefficients of our approach is on par with state-of-the-art regression techniques, while scaling notably better and also being competitive with other time-aware RS in terms of prediction performance. We illustrate FaStR's performance and interpretability on a large-scale behavioral study with smartphone user data.

Due to the drastic gap in complexity between sequential and batch statistical learning, recent work has studied a smoothed sequential learning setting, where Nature is constrained to select contexts with density bounded by 1/{\sigma} with respect to a known measure {\mu}. Unfortunately, for some function classes, there is an exponential gap between the statistically optimal regret and that which can be achieved efficiently. In this paper, we give a computationally efficient algorithm that is the first to enjoy the statistically optimal log(T/{\sigma}) regret for realizable K-wise linear classification. We extend our results to settings where the true classifier is linear in an over-parameterized polynomial featurization of the contexts, as well as to a realizable piecewise-regression setting assuming access to an appropriate ERM oracle. Somewhat surprisingly, standard disagreement-based analyses are insufficient to achieve regret logarithmic in 1/{\sigma}. Instead, we develop a novel characterization of the geometry of the disagreement region induced by generalized linear classifiers. Along the way, we develop numerous technical tools of independent interest, including a general anti-concentration bound for the determinant of certain matrix averages.