Many data sets are cross-sectional and represent a single slice of time. However, we also have data collected over many periods - weekly sales data, for instance. This is an example of time series data. Time series analysis is a specialized branch of statistics used extensively in fields such as Econometrics and Operations Research. Unfortunately, most Marketing Researchers and Data Scientists still have had little exposure to it.

Orange is a component based data mining and machine learning software suite written in the Python language. It is an Open source data visualization and analysis for novice and experts. Data mining can be done through visual programming or Python scripting. It has components for machine learning. There are add ons for bioinformatics and text mining.

We consider the problem of estimating the parameters of a linear univariate autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze the performance of the $\ell_1$-regularized least squares as well as a greedy estimator of the parameters and characterize the sampling trade-offs required for stable recovery in the non-asymptotic regime. In particular, we show that for a fixed sparsity level, stable recovery of AR parameters is possible when the number of samples scale sub-linearly with the AR order. Our results improve over existing sampling complexity requirements in AR estimation using the LASSO, when the sparsity level scales faster than the square root of the model order. We further derive sufficient conditions on the sparsity level that guarantee the minimax optimality of the $\ell_1$-regularized least squares estimate. Applying these techniques to simulated data as well as real-world datasets from crude oil prices and traffic speed data confirm our predicted theoretical performance gains in terms of estimation accuracy and model selection.

Radio signal recognition in dense and complex multi-user spectrum environments is an important tool for optimizing spectrum utilization, identifying and minimizing interference, enforcing spectrum policy, and implementing effective radio sensing and coordination systems. Classical approaches to the problem focus on energy detection and the use of expert features and decision criteria to identify and categorize specific modulation types [2] [1]. These approaches rely on prior knowledge of signal properties, features, and decision statistics to separate known modulations and are typically derived under simplified analytic hardware, propagation, radio environment models. We recently demonstrated the viability of naive feature learning for supervised radio classification systems [14] which allows for joint feature and classifier learning given labeled datasets and examples. In this case we were able to outperform traditional expert decision statistic based classification in sensitivity and accuracy by a significant margin. This was a powerful result, providing significant performance improvements against current day solutions, but it still relied entirely on supervised learning and well curated training data. In the real world, and especially in the radio domain, we are faced with vast amounts of unlabeled example data available to our sensor and incomplete knowledge of class labels comprising ground truth. To address this problem we investigate alternative strategies for radio identification learning which rely less heavily on labeled training data and are capable of making sense of radio signals with either no or less labeled examples, potentially drastically reducing the burden of data curation on such a machine learning system for developers and maintainers, and allowing systems to recognize new signals and scale to to understand new environments over time.

The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including convex feasibility, linear complementarity, and regression with constraint sets. When a feasible point does not exist, solution methods that proceed by minimizing a proximity function can be used to obtain optimal approximate solutions to the problem. We present an extension of the proximity function approach that generalizes the linear split feasibility problem to allow for non-linear mappings. Our algorithm is based on the principle of majorization-minimization, is amenable to quasi-Newton acceleration, and comes complete with convergence guarantees under mild assumptions. Furthermore, we show that the Euclidean norm appearing in the proximity function of the non-linear split feasibility problem can be replaced by arbitrary Bregman divergences. We explore several examples illustrating the merits of non-linear formulations over the linear case, with a focus on optimization for intensity-modulated radiation therapy.

In this paper, we propose two {\bf accelerated stochastic subgradient} methods for stochastic non-strongly convex optimization problems by leveraging a generic local error bound condition. The novelty of the proposed methods lies at smartly leveraging the recent historical solution to tackle the variance in the stochastic subgradient. The key idea of both methods is to iteratively solve the original problem approximately in a local region around a recent historical solution with size of the local region gradually decreasing as the solution approaches the optimal set. The difference of the two methods lies at how to construct the local region. The first method uses an explicit ball constraint and the second method uses an implicit regularization approach. For both methods, we establish the improved iteration complexity in a high probability for achieving an $\epsilon$-optimal solution. Besides the improved order of iteration complexity with a high probability, the proposed algorithms also enjoy a logarithmic dependence on the distance of the initial solution to the optimal set. We also consider applications in machine learning and demonstrate that the proposed algorithms enjoy faster convergence than the traditional stochastic subgradient method. For example, when applied to the $\ell_1$ regularized polyhedral loss minimization (e.g., hinge loss, absolute loss), the proposed stochastic methods have a logarithmic iteration complexity.

Despite significant progress made over the past twenty five years, unconstrained face verification remains a challenging problem. This paper proposes an approach that couples a deep CNN-based approach with a low-dimensional discriminative embedding learned using triplet probability constraints to solve the unconstrained face verification problem. Aside from yielding performance improvements, this embedding provides significant advantages in terms of memory and for post-processing operations like subject specific clustering. Experiments on the challenging IJB-A dataset show that the proposed algorithm performs comparably or better than the state of the art methods in verification and identification metrics, while requiring much less training data and training time. The superior performance of the proposed method on the CFP dataset shows that the representation learned by our deep CNN is robust to extreme pose variation. Furthermore, we demonstrate the robustness of the deep features to challenges including age, pose, blur and clutter by performing simple clustering experiments on both IJB-A and LFW datasets.

TensorFlow is an open source software library for Machine Intelligence. The independent recipes in this book will teach you how to use TensorFlow for complex data computations and will help you gain more insights into your data than ever before. We'll start with the fundamentals of the TensorFlow library and you will learn about variables, matrices, and various data sources. Moving ahead, you will get hands-on experience of Linear Regression techniques with TensorFlow. The next chapters cover important high-level concepts such as neural networks, CNN, RNN, and NLP through real-world examples in every recipe.

In many cases, you may think that you have a Big Data problem, when in reality you just have a lot of data that a simple sampling can result in great accuracy. In todays blog, I decided to use office room occupancy dataset provided by"Accurate occupancy detection of an office room from light, temperature, humidity and CO2 measurements using statistical learning models. The dataset provided has 6 independent variables (predictors): date with timestamp; temperature of the room in Celsius; relative humidity in percent, light in Lux; CO2 in ppm, and humidity ratio or the ratio between temperature and humidity. The occupancy is a categorical variable with 2 levels: 0 for not occupied; and 1 for occupied. The occupancy has been measured every minutes, for the period of February 11, 2015 to February 18, 2015, and its dataset size is 9,752. The question I want to investigate is can a small random sample produce performance as good as large sample? For the model, I will build a Deep Feed ...

The classification of MRI images according to the anatomical field of view is a necessary task to solve when faced with the increasing quantity of medical images. In parallel, advances in deep learning makes it a suitable tool for computer vision problems. Using a common architecture (such as AlexNet) provides quite good results, but not sufficient for clinical use. Improving the model is not an easy task, due to the large number of hyper-parameters governing both the architecture and the training of the network, and to the limited understanding of their relevance. Since an exhaustive search is not tractable, we propose to optimize the network first by random search, and then by an adaptive search based on Gaussian Processes and Probability of Improvement. Applying this method on a large and varied MRI dataset, we show a substantial improvement between the baseline network and the final one (up to 20\% for the most difficult classes).