I am trying to find a solution to the decision boundary in QDA. The question was already asked and answered for LDA, and the solution provided by amoeba to compute this using the "standard Gaussian way" worked well. However, I am applying the same technique for a 2 class, 2 feature QDA and am having trouble. Would someone be able to check my work and let me know if this approach is correct? Where $\delta_l$ is the discriminant score for some observation $\mathbf{x}$ belonging to class $l$ which could be 0 or 1 in this 2 class problem.

Representation of human actions as a sequence of human body movements or action attributes enables the development of models for human activity recognition and summarization. We present an extension of the low-rank representation (LRR) model, termed the clustering-aware structure-constrained low-rank representation (CS-LRR) model, for unsupervised learning of human action attributes from video data. Our model is based on the union-of-subspaces (UoS) framework, and integrates spectral clustering into the LRR optimization problem for better subspace clustering results. We lay out an efficient linear alternating direction method to solve the CS-LRR optimization problem. We also introduce a hierarchical subspace clustering approach, termed hierarchical CS-LRR, to learn the attributes without the need for a priori specification of their number. By visualizing and labeling these action attributes, the hierarchical model can be used to semantically summarize long video sequences of human actions at multiple resolutions. A human action or activity can also be uniquely represented as a sequence of transitions from one action attribute to another, which can then be used for human action recognition. We demonstrate the effectiveness of the proposed model for semantic summarization and action recognition through comprehensive experiments on five real-world human action datasets.

The vast majority of current machine learning algorithms are designed to predict single responses or a vector of responses, yet many types of response are more naturally organized as matrices or higher-order tensor objects where characteristics are shared across modes. We present a new machine learning algorithm BaTFLED (Bayesian Tensor Factorization Linked to External Data) that predicts values in a three-dimensional response tensor using input features for each of the dimensions. BaTFLED uses a probabilistic Bayesian framework to learn projection matrices mapping input features for each mode into latent representations that multiply to form the response tensor. By utilizing a Tucker decomposition, the model can capture weights for interactions between latent factors for each mode in a small core tensor. Priors that encourage sparsity in the projection matrices and core tensor allow for feature selection and model regularization. This method is shown to far outperform elastic net and neural net models on 'cold start' tasks from data simulated in a three-mode structure. Additionally, we apply the model to predict dose-response curves in a panel of breast cancer cell lines treated with drug compounds that was used as a Dialogue for Reverse Engineering Assessments and Methods (DREAM) challenge.

This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive procedure based on cross validation, and establish its convergence rate under the Frobenius norm. The convergence rates under other matrix norms are also established. This method also enjoys the advantage of fast computation for large-scale problems, via a coordinate descent algorithm. Numerical merits are illustrated using both simulated and real datasets. In particular, it performs favorably on an HIV brain tissue dataset and an ADHD resting-state fMRI dataset.

Text documents can be described by a number of abstract concepts such as semantic category, writing style, or sentiment. Machine learning (ML) models have been trained to automatically map documents to these abstract concepts, allowing to annotate very large text collections, more than could be processed by a human in a lifetime. Besides predicting the text's category very accurately, it is also highly desirable to understand how and why the categorization process takes place. In this paper, we demonstrate that such understanding can be achieved by tracing the classification decision back to individual words using layer-wise relevance propagation (LRP), a recently developed technique for explaining predictions of complex non-linear classifiers. We train two word-based ML models, a convolutional neural network (CNN) and a bag-of-words SVM classifier, on a topic categorization task and adapt the LRP method to decompose the predictions of these models onto words. Resulting scores indicate how much individual words contribute to the overall classification decision. This enables one to distill relevant information from text documents without an explicit semantic information extraction step. We further use the word-wise relevance scores for generating novel vector-based document representations which capture semantic information. Based on these document vectors, we introduce a measure of model explanatory power and show that, although the SVM and CNN models perform similarly in terms of classification accuracy, the latter exhibits a higher level of explainability which makes it more comprehensible for humans and potentially more useful for other applications.

Last week, we learned about Random Forest Algorithm. Now we know it helps us reduce a model's variance by building models on resampled data and thereby increases its generalization capability.

The structure-function relationship is fundamental to our understanding of biological systems at all levels, and drives most, if not all, techniques for detecting, diagnosing, and treating a disease. The predominant means of collecting structure/function data in biomedicine is reductionist and has thus led to a proliferation of complex data (for example, gene expression arrays, digital images) that captures only a fraction of the structure/function relationship. Gene sequence and expression data illustrates the structure and activities of individual genes but does not explain how these genes collaborate to control cellular and tissue-scale functions. As a result, despite the abundance of molecular details known about wound healing, for example, it is virtually impossible to accurately predict the final functional state of a healing wound.36 This illustrates a need to build models that represent the structural organization at the organ, tissue, cellular, and molecular levels. Furthermore, such models must capture relationships between these scales and relate them to the underlying functional state. Data-driven network/graph analysis is primed to decipher cellular interactions in the intricate relationship between protein-protein interactions, genetic changes, metabolic pathways, and chemical secretions, which comprise cellular events. When extended to the organ level, the key challenge would be to link the local and global structural properties of tissues to the overall morphology and function of a tissue. Only a systems-level understanding of the various cellular processes encompassing multiple biological levels will take into account the multidimensional complexity of these processes. If the principles governing biological organization on a morphological, spectral, local, and global scale can be deduced, the correlation between structural and molecular signaling within the tissue can be understood and applied to inform and accelerate studies of organ development and tissue regeneration. The cell-graph technique11,12,20 aims to learn structure-function relationship by modeling structural organization of a tissue/organ sample using graph theory. Its main hypothesis is that cells in a tissue/organ organize to perform a specific function.

Microsoft R Server 9.0, Microsoft's R distribution with added big-data, in-database, and integration capabilities, was released today and is now available for download to MSDN subscribers. This latest release is built on Microsoft R Open 3.3.2, This release includes a brand new R package for machine learning: MicrosoftML. This package provides state-of-the-art, fast and scalable machine learning algorithms for common data science tasks including featurization, classification and regression. Fast linear and logistic model functions based on the Stochastic Dual Coordinate Ascent method; Fast Forests, a random forest and quantile regression forest implementation based on FastRank, an efficient implementation of the MART gradient boosting algorithm; A neural network algorithm with support for custom, multilayer network topologies and GPU acceleration; One-class anomaly detection based on support vector machines. One-class anomaly detection based on support vector machines.

The diversity of IoT use cases demands a range of analytics capability, spanning from traditional descriptive analytics to more advanced predictive and prescriptive analytics. VIA supports an extensive set of analytic techniques that meet the demands of IoT. VIA Analytics includes all the key types of analytics – real-time, historical, predictive, and prescriptive – needed for IoT. It executes fast analytics in real-time to provide the context and insight needed for the fast decision-making required in IoT. Highlights of VIA's Analytic capabilities include: Time-series analysis provides insight into the behavior of IoT networks over time.

Explain what regularization is and why it is useful. What are the benefits and drawbacks of specific methods, such as ridge regression and LASSO? Explain what a local optimum is and why it is important in a specific context, such as k-means clustering. What are specific ways for determining if you have a local optimum problem? What can be done to avoid local optima?