Symmetry is the essential element of lifted inferencethat has recently demonstrated the possibility to perform very efficient inference in highly-connected, but symmetric probabilistic models. This raises the question, whether this holds for optimization problems in general.Here we show that for a large classof optimization methods this is actually the case.Specifically, we introduce the concept of fractionalsymmetries of convex quadratic programs (QPs),which lie at the heart of many AI and machine learning approaches,and exploit it to lift, i.e., to compress QPs.These lifted QPs can then be tackled with the usual optimization toolbox (off-the-shelf solvers, cutting plane algorithms,stochastic gradients etc.). If the original QP exhibitssymmetry, then the lifted one will generallybe more compact, and hence more efficient to solve.

Alzheimer's disease (AD) is a genetically complex neurodegenerative disease, which leads to irreversible brain damage, severe cognitive problems and ultimately death. A number of clinical trials and study initiatives have been set up to investigate AD pathology, leading to large amounts of high dimensional heterogeneous data (biomarkers) for analysis. This paper focuses on combining clinical features from different modalities, including medical imaging, cerebrospinal fluid (CSF), etc., to diagnose AD and predict potential progression. Due to privacy and legal issues involved with clinical research, the study cohort (number of patients) is relatively small, compared to thousands of available biomarkers (predictors). We propose a hybrid pathological analysis model, which integrates manifold learning and Random Vector functional-link network (RVFL) so as to achieve better ability to extract discriminant information with limited training materials. Furthermore, we model (current and future) cognitive healthiness as a regression problem about age. By comparing the difference between predicted age and actual age, we manage to show statistical differences between different pathological stages. Verification tests are conducted based on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. Extensive comparison is made against different machine learning algorithms, i.e. Support Vector Machine (SVM), Random Forest (RF), Decision Tree and Multilayer Perceptron (MLP). Experimental results show that our proposed algorithm achieves better results than the comparison targets, which indicates promising robustness for practical clinical implementation.

Stacking (also called meta ensembling) is a model ensembling technique used to combine information from multiple predictive models to generate a new model. Often times the stacked model (also called 2nd-level model) will outperform each of the individual models due its smoothing nature and ability to highlight each base model where it performs best and discredit each base model where it performs poorly. For this reason, stacking is most effective when the base models are significantly different. Here I provide a simple example and guide on how stacking is most often implemented in practice. Feel free to follow this article using the related code and datasets here in the Machine Learning Problem Bible.

Statistical downscaling of global climate models (GCMs) allows researchers to study local climate change effects decades into the future. A wide range of statistical models have been applied to downscaling GCMs but recent advances in machine learning have not been explored. In this paper, we compare four fundamental statistical methods, Bias Correction Spatial Disaggregation (BCSD), Ordinary Least Squares, Elastic-Net, and Support Vector Machine, with three more advanced machine learning methods, Multi-task Sparse Structure Learning (MSSL), BCSD coupled with MSSL, and Convolutional Neural Networks to downscale daily precipitation in the Northeast United States. Metrics to evaluate of each method's ability to capture daily anomalies, large scale climate shifts, and extremes are analyzed. We find that linear methods, led by BCSD, consistently outperform non-linear approaches. The direct application of state-of-the-art machine learning methods to statistical downscaling does not provide improvements over simpler, longstanding approaches.

Our learning task: Given a training set S {(x1 , y1), (x2 , y2), . . . The simplest case: y { 1, 1} called binary classification problem If y is a real number it becomes a regression problem More general case, y can be a vector and each element is drawn from a finite set.

Given a training set with binary classification, the Support Vector Machine identifies the hyperplane maximizing the margin between the two classes of training data. This general formulation is useful in that it can be applied without regard to variance differences between the classes. Ignoring these differences is not optimal, however, as the general SVM will give the class with lower variance an unjustifiably wide berth. This increases the chance of misclassification of the other class and results in an overall loss of predictive performance. An alternate construction is proposed in which the margins of the separating hyperplane are different for each class, each proportional to the standard deviation of its class along the direction perpendicular to the hyperplane. The construction agrees with the SVM in the case of equal class variances. This paper will then examine the impact to the dual representation of the modified constraint equations.

As enjoying the closed form solution, least squares support vector machine (LSSVM) has been widely used for classification and regression problems having the comparable performance with other types of SVMs. However, LSSVM has two drawbacks: sensitive to outliers and lacking sparseness. Robust LSSVM (R-LSSVM) overcomes the first partly via nonconvex truncated loss function, but the current algorithms for R-LSSVM with the dense solution are faced with the second drawback and are inefficient for training large-scale problems. In this paper, we interpret the robustness of R-LSSVM from a re-weighted viewpoint and give a primal R-LSSVM by the representer theorem. The new model may have sparse solution if the corresponding kernel matrix has low rank. Then approximating the kernel matrix by a low-rank matrix and smoothing the loss function by entropy penalty function, we propose a convergent sparse R-LSSVM (SR-LSSVM) algorithm to achieve the sparse solution of primal R-LSSVM, which overcomes two drawbacks of LSSVM simultaneously. The proposed algorithm has lower complexity than the existing algorithms and is very efficient for training large-scale problems. Many experimental results illustrate that SR-LSSVM can achieve better or comparable performance with less training time than related algorithms, especially for training large scale problems.

The output of the face detector is scaled to 90x90 and fed directly to the facial expression analysis system (see Figure 1). The system is essentially the same as the one used for Automatic FACS coding. First the face image is passed through a bank of Gabor filters at 8 orientations and 9 scales (2-32 pixels/cycle at 0.5 octave steps). The filterbank representations are then channeled to a classifier to code the image in terms of a set of expression dimensions. We have found support vector machines to be very effective for classifying facial expressions (Littlewort et al., in press, Bartlett et al., 2003).

Uncertainty analysis in the form of probabilistic forecasting can provide significant improvements in decision making processes in the smart power gird for better integrating renewable energies such as wind. Whereas point forecasting provides a single expected value, probabilistic forecasts provide more information in the form of quantiles, prediction intervals, or full predictive densities. This paper analyzes the effectiveness of an approach for nonparametric probabilistic forecasting of wind power that combines support vector machines and nonlinear quantile regression with non-crossing constraints. A numerical case study is conducted using publicly available wind data from the Global Energy Forecasting Competition 2014. Multiple quantiles are estimated to form 20%, 40%, 60% and 80% prediction intervals which are evaluated using the pinball loss function and reliability measures. Three benchmark models are used for comparison where results demonstrate the proposed approach leads to significantly better performance while preventing the problem of overlapping quantile estimates.

Two popular approaches for distributed training of SVMs on big data are parameter averaging and alternating direction method of multipliers (ADMM). Parameter averaging is efficient but suffers from loss of accuracy with increase in number of partitions, while ADMM in the feature space is accurate but suffers from slow convergence. In this paper, we report a hybrid approach called weighted parameter averaging (WPA), which optimizes the regularized hinge loss with respect to weights on parameters. The problem is shown to be same as solving SVM in a projected space. We also demonstrate an O(1/N) stability bound on final hypothesis given by WPA, using novel proof techniques. Experimental results on a variety of toy and real world datasets show that our approach is significantly more accurate than parameter averaging for high number of partitions. It is also seen the proposed method enjoys much faster convergence compared to ADMM in feature space.