In this paper, we investigate the problem of exploiting global information to improve the performance of SVMs on large scale classification problems. We first present a unified general framework for the existing min-max machine methods in terms of within-class dispersions and between-class dispersions. By defining a new within-class dispersion measure, we then propose a novel max-margin ratio m...

Introduction. In my note on A 5 curve theorem generalizing the theorem of Carnot, I introduced the notion of curve cross ratio. This extension of the ordinary cross ratio is the simplest situationally invariant (3.4) case of the generalized or hypersurface cross ratio of n + l pairs of hypersurfaces in w-space which is the subject of the following lines. The generalized cross ratio is a t the s...

In a seminal paper of Charikar et al. on the smallest grammar problem, the authors derive upper and lower bounds on the approximation ratios for several grammar-based compressors. Here we improve the lower bound for the famous RePair algorithm from Ω( √ log n) to Ω(log n/ log log n). The family of words used in our proof is defined over a binary alphabet, while the lower bound from Charikar et ...

We link the reverse KL divergence with adversarial learning. This insight enables learning to synthesize realistic samples in two settings: (i) Given a set of samples from the true distribution, an adversarially learned likelihood-ratio and a new entropy bound are used to learn a GAN model, that improves synthesized sample quality relative to previous GAN variants. (ii) Given an unnormalized di...

Isotope Ratio Mass Spectrometry (IRMS) is a specialized technique used to provide information about the geographic, chemical, and biological origins of substances. The ability to determine the source of an organic substance stems from the relative isotopic abundances of the elements which comprise the material. Because the isotope ratios of elements such as carbon, hydrogen, oxygen, sulfur, and...

The role of mathematics in empirical science is puzzling, mysterious, and in my opinion has defied rational explanation. Why mathematics should be so enormously productive and effective in the handling of empirical phenomena is clearly an important foundational problem in science, but one for the most part that has been ignored. This is somewhat surprising given the rich theory and the abundanc...

The competitive complexity ratio is the worst case ratio of the regret of a data-driven model to that obtained by a model which benefits from side information. The side information bounds the sizes of unknown parameters. The ratio requires the use of a variation on parametric complexity, which we call the unconditional parametric complexity. We show that the optimal competitive complexity ratio...

Prothrombin time can be measured roughly on whole blood as in neonates, but is more commonly measured from plasma. Blood is taken into a vacutainer containing liquid citrate. Citrate acts as an anticoagulant by consuming all the calcium in the sample. The blood is mixed and centrifuged to separate blood cells from the plasma. The plasma is placed in a coagulation machine which takes a sample of...

Objective: To present a geometric ruler to determine predictive values of binary diagnostic test results from prevalence, sensitivity and specificity without calculation. Methods: On logarithmic scale the relationships between pre-/post-test odds and the likelihood ratio as well as sensitivity, speci ficity and the likelihood ratio appear as simple linear (additive) equations. Results: Each of ...