Notes on Regularized Least Squares

This is a collection of information about regularized least squares (RLS). The facts here are not new results, but we have not seen them usefully collected together before. A key goal of this work is to demonstrate that with RLS, we get certain things for free: if we can solve a single supervised RLS problem, we can search for a good regularization parameter lambda at essentially no additional cost.The discussion in this paper applies to dense regularized least squares, where we work with matrix factorizations of the data or kernel matrix. It is also possible to work with iterative methods such as conjugate gradient, and this is frequently the method of choice for large data sets in high dimensions with very few nonzero dimensions per point, such as text classifciation tasks. The results discussed here do not apply to iterative methods, which have different design tradeoffs.We present the results in greater detail than strictly necessary, erring on the side of showing our work. We hope that this will be useful to people trying to learn more about linear algebra manipulations in the machine learning context

ACA Implementation Monitoring and Tracking: New York Site Visit Report

Examines New York's progress in implementing the 2010 federal healthcare reform, including an executive order to establish a health insurance exchange, legislation to enact insurance reforms, and the debate over implementing the Basic Health Program

Puromycin Sensitivity of Ribosomal Label after Incorporation of 14C-Labelled Amino Acids into Isolated Mitochondria from Neurospora crassa

Radioactive amino acids were incorporated into isolated mitochondria from Neurospora crassa. Then the mitochondrial ribosomes were isolated and submitted to density gradient centrifugation. A preferential labelling of polysomes was observed. However, when the mitochondrial suspension was treated with puromycin after amino acid incorporation, no radioactivity could be detected in either the monosomes or the polysomes. The conclusion is drawn that isolated mitochondria under these conditions do not incorporate significant amounts of amino acids into proteins of their ribosomes

A Unifying View of Multiple Kernel Learning

Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization strategies. In this paper we present a unifying general optimization criterion for multiple kernel learning and show how existing formulations are subsumed as special cases. We also derive the criterion's dual representation, which is suitable for general smooth optimization algorithms. Finally, we evaluate multiple kernel learning in this framework analytically using a Rademacher complexity bound on the generalization error and empirically in a set of experiments

Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learning-based premise selection in two ways. First, a newly available minimal dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATP-based re-verification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a benchmark consisting of 2078 large-theory mathematical problems is constructed,extending the older MPTP Challenge benchmark. The combined effect of the techniques results in a 50% improvement on the benchmark over the Vampire/SInE state-of-the-art system for automated reasoning in large theories.Comment: 26 page

Inhibition in multiclass classification

The role of inhibition is investigated in a multiclass support vector machine formalism inspired by the brain structure of insects. The so-called mushroom bodies have a set of output neurons, or classification functions, that compete with each other to encode a particular input. Strongly active output neurons depress or inhibit the remaining outputs without knowing which is correct or incorrect. Accordingly, we propose to use a classification function that embodies unselective inhibition and train it in the large margin classifier framework. Inhibition leads to more robust classifiers in the sense that they perform better on larger areas of appropriate hyperparameters when assessed with leave-one-out strategies. We also show that the classifier with inhibition is a tight bound to probabilistic exponential models and is Bayes consistent for 3-class problems. These properties make this approach useful for data sets with a limited number of labeled examples. For larger data sets, there is no significant comparative advantage to other multiclass SVM approaches

AN ENZYMATIC FUNCTION ASSOCIATED WITH TRANSFORMATION OF FIBROBLASTS BY ONCOGENIC VIRUSES : I. CHICK EMBRYO FIBROBLAST CULTURES TRANSFORMED BY AVIAN RNA TUMOR VIRUSES

Chick embryo fibroblast cultures develop fibrinolytic activity after transformation by Rous sarcoma virus (RSV). This fibrinolytic activity is not present in normal cultures, and it does not appear after infection with either nontransforming strains of avian leukosis viruses or cytocidal RNA and DNA viruses. In cultures infected with a temperature sensitive mutant of RSV the onset of fibrinolysis appears after exposure to permissive temperatures and precedes by a short interval the appearance of morphological evidence of transformation. See PDF for Structure The rate of fibrinolysis in transformed cultures depends on the nature of the serum that is present in the growth medium: some sera (e.g., monkey or chicken serum) promote high enzymatic activity, while others (calf, fetal bovine) do not. Some sera contain inhibitors of the fibrinolysin. Based on the effect of a small number of known inhibitors, at least one step of the fibrinolytic process shows specificity resembling that of trypsin. The sera of sarcoma-bearing chickens contain an inhibitor of the fibrinolysin, whereas normal chicken sera do not. For general discussion, conclusions, and summary see the accompanying paper, part II, (J. Exp. Med. 137:112)