4,153 research outputs found
Generalised Mixability, Constant Regret, and Bayesian Updating
Mixability of a loss is known to characterise when constant regret bounds are
achievable in games of prediction with expert advice through the use of Vovk's
aggregating algorithm. We provide a new interpretation of mixability via convex
analysis that highlights the role of the Kullback-Leibler divergence in its
definition. This naturally generalises to what we call -mixability where
the Bregman divergence replaces the KL divergence. We prove that
losses that are -mixable also enjoy constant regret bounds via a
generalised aggregating algorithm that is similar to mirror descent.Comment: 12 page
Generalized Mixability via Entropic Duality
Mixability is a property of a loss which characterizes when fast convergence
is possible in the game of prediction with expert advice. We show that a key
property of mixability generalizes, and the exp and log operations present in
the usual theory are not as special as one might have thought. In doing this we
introduce a more general notion of -mixability where is a general
entropy (\ie, any convex function on probabilities). We show how a property
shared by the convex dual of any such entropy yields a natural algorithm (the
minimizer of a regret bound) which, analogous to the classical aggregating
algorithm, is guaranteed a constant regret when used with -mixable
losses. We characterize precisely which have -mixable losses and
put forward a number of conjectures about the optimality and relationships
between different choices of entropy.Comment: 20 pages, 1 figure. Supersedes the work in arXiv:1403.2433 [cs.LG
Fast rates in statistical and online learning
The speed with which a learning algorithm converges as it is presented with
more data is a central problem in machine learning --- a fast rate of
convergence means less data is needed for the same level of performance. The
pursuit of fast rates in online and statistical learning has led to the
discovery of many conditions in learning theory under which fast learning is
possible. We show that most of these conditions are special cases of a single,
unifying condition, that comes in two forms: the central condition for 'proper'
learning algorithms that always output a hypothesis in the given model, and
stochastic mixability for online algorithms that may make predictions outside
of the model. We show that under surprisingly weak assumptions both conditions
are, in a certain sense, equivalent. The central condition has a
re-interpretation in terms of convexity of a set of pseudoprobabilities,
linking it to density estimation under misspecification. For bounded losses, we
show how the central condition enables a direct proof of fast rates and we
prove its equivalence to the Bernstein condition, itself a generalization of
the Tsybakov margin condition, both of which have played a central role in
obtaining fast rates in statistical learning. Yet, while the Bernstein
condition is two-sided, the central condition is one-sided, making it more
suitable to deal with unbounded losses. In its stochastic mixability form, our
condition generalizes both a stochastic exp-concavity condition identified by
Juditsky, Rigollet and Tsybakov and Vovk's notion of mixability. Our unifying
conditions thus provide a substantial step towards a characterization of fast
rates in statistical learning, similar to how classical mixability
characterizes constant regret in the sequential prediction with expert advice
setting.Comment: 69 pages, 3 figure
Generalised Pinsker Inequalities
We generalise the classical Pinsker inequality which relates variational
divergence to Kullback-Liebler divergence in two ways: we consider arbitrary
f-divergences in place of KL divergence, and we assume knowledge of a sequence
of values of generalised variational divergences. We then develop a best
possible inequality for this doubly generalised situation. Specialising our
result to the classical case provides a new and tight explicit bound relating
KL to variational divergence (solving a problem posed by Vajda some 40 years
ago). The solution relies on exploiting a connection between divergences and
the Bayes risk of a learning problem via an integral representation.Comment: 21 pages, 3 figures, accepted to COLT 200
The Revolution Will Be Open-Source: How 3D Bioprinting Can Change 3D Cell Culture
(First paragraph) The development of three-dimensional culture scaffolds represents a revolutionary step forward for in vitro culture systems. Various synthetic and naturally occurring substrates have been developed that support 3D growth of cells. In most fields, including mammary gland biology and tumorigenesis, the two most common substrates used are the basement membrane rich extracellur matrix (ECM) isolated from EngelbrethHolm-Swarm (EHS) mouse sarcomas (e.g. Matrigel) and collagen extracted from rat-tails. The processes of 3D culture in these two substrates has remained unchanged for nearly half a century: cells are either mixed with unpolymerized matrix to disperse them randomly throughout the substrate upon polymerization or overlaid randomly on top of a preformed hydrogel. While effective in generating organoid/tumoroid structures, the random nature of these processes has many drawbacks that limit the reproducibility and tunability of the experimental design. Furthermore, random cellular distributions limit the utility of these substrates for studying interactions within the cellular microenvironment, which have been shown to be critical for the control of stem and cancer cell function [1]
Improved Models of Cable-to-Post Attachments for High-Tension Cable Barriers
Computer simulation models were developed to analyze and evaluate a new cable-to-post attachment for high-tension cable barriers. The models replicated the performance of a keyway bolt currently used in the design of a high-tension cable median barrier being developed at the Midwest Roadside Safety Facility. Component tests of the keyway bolts were simulated and compared to the component test results. Accurate friction, fracture strain, and stress-strain material properties were determined for a solid element model of the keyway bolt by applying actual load curve measured from the test to a simulated pull cable. By simulating the material properties of the solid element keyway bolt in bending, torsion, and tension of a rod, load curves were developed for a simplified beam element model of the keyway bolt as well. When material properties were finalized, the solid and beam element models of the keyway bolt were inserted in bogie test models and simulated again. By analyzing the bogie testing results, it was determined that due to the very small size of the keyway bolt and potential contact difficulties, solid element models of the keyway bolt may be impractical for full-scale simulation purposes. However, the beam element models were determined to be advantageous and had a very small computational cost in comparison
Continued Development of a Non-Proprietary, High-Tension, Cable End Terminal System
A non-proprietary, cable guardrail system is currently under development for the Midwest States Pooled Fund Program. A cable guardrail end terminal was necessary to accompany the cable guardrail system. The objective of this research project was to develop design recommendations for the cable end terminal. Bogie testing that was previously completed on a design concept indicated delayed cable release, which was an undesired performance that led to vehicle instabilities. Several design changes were recommended for better end terminal performance and to reflect the changes made to the cable median barrier. An LS-DYNA model of the modified cable end terminal was developed. Simulations of 0- and 15-degree impacts on the end of the cable anchor bracket with a bogie model indicated that the cables would release easily and not induce vehicle instabilities. This behavior still needs to be verified through bogie and full-scale crash testing. Simulations of a 25-degree reverse impact between post nos. 2 and 3 with small car models indicated that cables did not release easily and may interlock around the car resulting in excessive vehicle decelerations or instabilities. Simulations of various line post designs found that the MWP and weakened MWP have lower forces and energies during impact than the S3x5.7 posts used in previous three-cable end terminals. This finding would suggest improved performance with respect to vehicle override and instability. However, vehicle simulations with multiple line posts impacted were inconclusive. Further design modifications, evaluation, and testing are recommended
Continued Development of a Non-Proprietary, High-Tension, Cable End Terminal System
A non-proprietary, cable guardrail system is currently under development for the Midwest States Pooled Fund Program. A cable guardrail end terminal was necessary to accompany the cable guardrail system. The objective of this research project was to develop design recommendations for the cable end terminal. Bogie testing that was previously completed on a design concept indicated delayed cable release, which was an undesired performance that led to vehicle instabilities. Several design changes were recommended for better end terminal performance and to reflect the changes made to the cable median barrier. An LS-DYNA model of the modified cable end terminal was developed. Simulations of 0- and 15-degree impacts on the end of the cable anchor bracket with a bogie model indicated that the cables would release easily and not induce vehicle instabilities. This behavior still needs to be verified through bogie and full-scale crash testing. Simulations of a 25-degree reverse impact between post nos. 2 and 3 with small car models indicated that cables did not release easily and may interlock around the car resulting in excessive vehicle decelerations or instabilities. Simulations of various line post designs found that the MWP and weakened MWP have lower forces and energies during impact than the S3x5.7 posts used in previous three-cable end terminals. This finding would suggest improved performance with respect to vehicle override and instability. However, vehicle simulations with multiple line posts impacted were inconclusive. Further design modifications, evaluation, and testing are recommended
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