In machine learning, there's something called the "No Free Lunch" theorem. In a nutshell, it states that no one algorithm works best for every problem, and it's especially relevant for supervised learning (i.e. For example, you can't say that neural networks are always better than decision trees or vice-versa. There are many factors at play, such as the size and structure of your dataset. As a result, you should try many different algorithms for your problem, while using a hold-out "test set" of data to evaluate performance and select the winner.

Let us type in "energy" in the search box. That will bring up Energy Efficiency Regression data as shown in Figure 7. Let's drag it and drop it on to the workspace.

Stochastic Gradient Descent (SGD) with small mini-batch is a key component in modern large-scale learning. However, its efficiency has not been easy to analyze as most theoretical results require adaptive rates and show convergence rates far slower than that for gradient descent, making computational comparisons difficult. In this paper we aim to clarify the issue of fast SGD convergence. The key observation is that most modern architectures are over-parametrized and are trained to interpolate the data by driving the empirical loss close to zero. While it is still unclear why these interpolated solutions perform well on test data, we show that these regimes allow for very fast convergence of SGD, comparable in the number of iterations to full gradient descent. Specifically, consider the setting with a quadratic objective function, or a general objective function in the proximity of a minimum, where the quadratic term is dominant. First, we obtain the optimal convergence rate for any mini-batch SGD and derive the optimal step size as a function of the batch size $m$. Second, we show: (1) $m=1$ is optimal in terms of number of computations required to achieve any desired accuracy. (2) There is a critical mini-batch size $m^*$ such that: (2a) SGD iteration with batch size $m\leq m^*$ is nearly equivalent to $m$ iterations of batch size $1$. (2b) SGD iteration with mini-batch $m> m^*$ is nearly equivalent to a full gradient descent iteration. The critical mini-batch size can be viewed as the limit for effective mini-batch parallelization. It is also nearly independent of the data size, implying $O(n)$ acceleration over GD per unit of computation. These theoretical analyses are verified by experimental results. Finally, we show how the interpolation perspective and our results fit in the deep neural networks and discuss connections to adaptive rates for SGD and variance reduction.

For a graph representation of a dataset, a straightforward normality measure for a sample can be its graph degree. Considering a weighted graph, degree of a sample is the sum of the corresponding row's values in a similarity matrix. The measure is intuitive given the abnormal samples are usually rare and they are dissimilar to the rest of the data. In order to have an in-depth theoretical understanding, in this manuscript, we investigate the graph degree in spectral graph clustering based and kernel based point of views and draw connections to a recent kernel method for the two sample problem. We show that our analyses guide us to choose fully-connected graphs whose edge weights are calculated via universal kernels. We show that a simple graph degree based unsupervised anomaly detection method with the above properties, achieves higher accuracy compared to other unsupervised anomaly detection methods on average over 10 widely used datasets. We also provide an extensive analysis on the effect of the kernel parameter on the method's accuracy.

Now a days, the major challenge in machine learning is the `Big~Data' challenge. The big data problems due to large number of data points or large number of features in each data point, or both, the training of models have become very slow. The training time has two major components: Time to access the data and time to process (learn from) the data. In this paper, we have proposed one possible solution to handle the big data problems in machine learning. The idea is to reduce the training time through reducing data access time by proposing systematic sampling and cyclic/sequential sampling to select mini-batches from the dataset. To prove the effectiveness of proposed sampling techniques, we have used Empirical Risk Minimization, which is commonly used machine learning problem, for strongly convex and smooth case. The problem has been solved using SAG, SAGA, SVRG, SAAG-II and MBSGD (Mini-batched SGD), each using two step determination techniques, namely, constant step size and backtracking line search method. Theoretical results prove the same convergence for systematic sampling, cyclic sampling and the widely used random sampling technique, in expectation. Experimental results with bench marked datasets prove the efficacy of the proposed sampling techniques.

Tree ensembles are flexible predictive models that can capture relevant variables and to some extent their interactions in a compact and interpretable manner. Most algorithms for obtaining tree ensembles are based on versions of boosting or Random Forest. Previous work showed that boosting algorithms exhibit a cyclic behavior of selecting the same tree again and again due to the way the loss is optimized. At the same time, Random Forest is not based on loss optimization and obtains a more complex and less interpretable model. In this paper we present a novel method for obtaining compact tree ensembles by growing a large pool of trees in parallel with many independent boosting threads and then selecting a small subset and updating their leaf weights by loss optimization. We allow for the trees in the initial pool to have different depths which further helps with generalization. Experiments on real datasets show that the obtained model has usually a smaller loss than boosting, which is also reflected in a lower misclassification error on the test set.

Sparse alpha-norm regularization has many data-rich applications in Marketing and Economics. Alpha-norm, in contrast to lasso and ridge regularization, jumps to a sparse solution. This feature is attractive for ultra high-dimensional problems that occur in demand estimation and forecasting. The alpha-norm objective is nonconvex and requires coordinate descent and proximal operators to find the sparse solution. We study a typical marketing demand forecasting problem, grocery store sales for salty snacks, that has many dummy variables as controls. The key predictors of demand include price, equivalized volume, promotion, flavor, scent, and brand effects. By comparing with many commonly used machine learning methods, alpha-norm regularization achieves its goal of providing accurate out-of-sample estimates for the promotion lift effects. Finally, we conclude with directions for future research.

Many theoretical results on estimation of high dimensional time series require specifying an underlying data generating model (DGM). Instead, along the footsteps of~\cite{wong2017lasso}, this paper relies only on (strict) stationarity and $ \beta $-mixing condition to establish consistency of lasso when data comes from a $\beta$-mixing process with marginals having subgaussian tails. Because of the general assumptions, the data can come from DGMs different than standard time series models such as VAR or ARCH. When the true DGM is not VAR, the lasso estimates correspond to those of the best linear predictors using the past observations. We establish non-asymptotic inequalities for estimation and prediction errors of the lasso estimates. Together with~\cite{wong2017lasso}, we provide lasso guarantees that cover full spectrum of the parameters in specifications of $ \beta $-mixing subgaussian time series. Applications of these results potentially extend to non-Gaussian, non-Markovian and non-linear times series models as the examples we provide demonstrate. In order to prove our results, we derive a novel Hanson-Wright type concentration inequality for $\beta$-mixing subgaussian random vectors that may be of independent interest.

Computed tomography (CT) examinations are commonly used to predict lung nodule malignancy in patients, which are shown to improve noninvasive early diagnosis of lung cancer. It remains challenging for computational approaches to achieve performance comparable to experienced radiologists. Here we present NoduleX, a systematic approach to predict lung nodule malignancy from CT data, based on deep learning convolutional neural networks (CNN). For training and validation, we analyze >1000 lung nodules in images from the LIDC/IDRI cohort. All nodules were identified and classified by four experienced thoracic radiologists who participated in the LIDC project. NoduleX achieves high accuracy for nodule malignancy classification, with an AUC of ~0.99. This is commensurate with the analysis of the dataset by experienced radiologists. Our approach, NoduleX, provides an effective framework for highly accurate nodule malignancy prediction with the model trained on a large patient population. Our results are replicable with software available at http://bioinformatics.astate.edu/NoduleX.

Coherent uncertainty quantification is a key strength of Bayesian methods. But modern algorithms for approximate Bayesian posterior inference often sacrifice accurate posterior uncertainty estimation in the pursuit of scalability. This work shows that previous Bayesian coreset construction algorithms---which build a small, weighted subset of the data that approximates the full dataset---are no exception. We demonstrate that these algorithms scale the coreset log-likelihood suboptimally, resulting in underestimated posterior uncertainty. To address this shortcoming, we develop greedy iterative geodesic ascent (GIGA), a novel algorithm for Bayesian coreset construction that scales the coreset log-likelihood optimally. GIGA provides geometric decay in posterior approximation error as a function of coreset size, and maintains the fast running time of its predecessors. The paper concludes with validation of GIGA on both synthetic and real datasets, demonstrating that it reduces posterior approximation error by orders of magnitude compared with previous coreset constructions.