We show that every language in NP has a probablistic verifier checks membership proofs for it using logarithmic number of random bits and by examining constant the proof. If string is language, then there exists proof such accepts with probability 1 (i.e., choice its string). For strings not rejects provided “proof” at least 1/2. Our result builds upon improves recent Arora Safra [1998] whose verifiers examine nonconstant (though this very slowly growing function input length). As...

We give a new characterization of NP: the class NP contains exactly those languages L for which membership proofs (a proof that an input x is in ) can be verified probabilistically polynomial time using logarithmic number random bits and by reading sublogarithmic from proof. discuss implications this characterization; specifically, we show approximating Clique Independent Set, even very weak sense, NP-hard.

We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every c > 1 and given any n nodes ℛ 2 , randomized version of the finds (1 + 1/ )-approximation to optimum traveling salesman tour O(n (log ) O(c) time. When are d running increases (O(√ c)) d-1 ). c, is · poly(log ), that nearly linear . The algorithmm can be derandomized, but this by factor previous best algorithm problem (due Christofides) achieves 3/2-aproximation also give similar schemes...

The Extension for Community Healthcare Outcomes (ECHO) model was developed to improve access care underserved populations with complex health problems such as hepatitis C virus (HCV) infection. With the use of video-conferencing technology, ECHO program trains primary providers treat diseases.We conducted a prospective cohort study comparing treatment HCV infection at University New Mexico (UNM) clinic by clinicians 21 sites in rural areas and prisons Mexico. A total 407 patients chronic who...

Algorithms in varied fields use the idea of maintaining a distribution over certain set and multiplicative update rule to iteratively change these weights.Their analyses are usually very similar rely on an exponential potential function.In this survey we present simple meta-algorithm that unifies many disparate algorithms derives them as instantiations meta-algorithm.We feel since its analysis so simple, applications broad, it should be standard part courses, like "divide conquer."

The class PCP(f(n),g(n)) consists of all languages L for which there exists a polynomial-time probabilistic oracle machine that used O(f(n)) random bits, queries O(g(n)) bits its and behaves as follows: If x in then an y such the accepts choices but if not every rejects with high probability. Arora Safra (1992) characterized NP PCP(log n, (loglogn)/sup O(1)/). authors improve on their result by showing NP=PCP(logn, 1). has following consequences: (1) MAXSNP-hard problems (e.g. metric TSP,...

We present a polynomial time approximation scheme for Euclidean TSP in /spl Rfr//sup 2/. Given any n nodes the plane and epsiv/>0, finds (1+/spl epsiv/)-approximation to optimum traveling salesman tour n/sup 0(1//spl epsiv/)/. When are d/, running increases n(O/spl tilde/(log/sup d-2/n)//spl epsiv//sup d-1/) The previous best algorithm problem (due Christofides (1976)) achieves 3/2-approximation time. also give similar schemes host of other problems, including Steiner Tree, k-TSP, Minimum...

We give a O (√log n )-approximation algorithm for the sparsest cut, edge expansion, balanced separator, and graph conductance problems. This improves (log of Leighton Rao (1988). use well-known semidefinite relaxation with triangle inequality constraints. Central to our analysis is geometric theorem about projections point sets in R d , whose proof makes essential phenomenon called measure concentration. also describe an interesting natural “approximate certificate” graph's which involves...

Review of turnover costs at a major medical center helps health care managers gain insights about the magnitude and determinants this managerial challenge assess implications for organizational effectiveness. Here, includes hiring, training, productivity loss costs. Minimum cost represented >5 percent total annual operating budget. Editor's Note: This article is being reprinted with permission from Health Care Management 29(1), 2-7. Copyright © 2009 Lippincott Williams & Wilkins.

Abstract The Extension for Community Healthcare Outcomes (ECHO) Model was developed by the University of New Mexico Health Sciences Center as a platform to deliver complex specialty medical care underserved populations through an innovative educational model team-based interdisciplinary development. Using state-of-the-art telehealth technology, best practice protocols, and case-based learning, ECHO trains supports primary providers develop knowledge self-efficacy on variety diseases. As...

Deep nets generalize well despite having more parameters than the number of training samples. Recent works try to give an explanation using PAC-Bayes and Margin-based analyses, but do not as yet result in sample complexity bounds better naive parameter counting. The current paper shows generalization that're orders magnitude practice. These rely upon new succinct reparametrizations trained net --- a compression that is explicit efficient. yield via simple compression-based framework...

We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., appear successful but the trained distribution be far from target in standard metrics. However, does occur for a weaker metric called neural net distance. It is also shown an approximate pure equilibrium exists discriminator/generator game special class generators with natural objectives when generator capacity and set sizes are moderate. This existence inspires MIX+GAN protocol,...

Topic Modeling is an approach used for automatic comprehension and classification of data in a variety settings, perhaps the canonical application uncovering thematic structure corpus documents. A number foundational works both machine learning theory have suggested probabilistic model documents, whereby documents arise as convex combination (i.e. distribution on) small topic vectors, each vector being on words word-frequencies). Similar models since been areas, Latent Dirichlet Allocation...

The Nonnegative Matrix Factorization (NMF) problem has a rich history spanning quantum mechanics, probability theory, data analysis, polyhedral combinatorics, communication complexity, demography, chemometrics, etc. In the past decade NMF become enormously popular in machine learning, where factorization is computed using variety of local search heuristics. Vavasis recently proved that this NP-complete. We initiate study when solvable polynomial time. Consider nonnegative m x n matrix $M$...

Semantic word embeddings represent the meaning of a via vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, have hand-tuned hyperparameters reweighting This paper proposes new generative model, dynamic version log-linear topic model Mnih Hinton (2007). The methodological novelty is to prior compute closed form expressions for statistics. provides theoretical justification models like PMI, word2vec, GloVe, as well some hyperparameter choices....

Topic models provide a useful method for dimensionality reduction and exploratory data analysis in large text corpora. Most approaches to topic model inference have been based on maximum likelihood objective. Efficient algorithms exist that approximate this objective, but they no provable guarantees. Recently, introduced bounds, these are not practical because inefficient robust violations of assumptions. In paper we present an algorithm is both practical. The produces results comparable the...

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods reminiscent the well-known word2vec embedding algorithm: leveraging availability pairs semantically "similar" points and "negative samples," learner forces inner product similar with each other be higher on average than negative samples. The current paper uses term contrastive learning for such algorithms presents a...

Many of the estimated thirty-two million Americans expected to gain coverage under Affordable Care Act are likely have high levels unmet need because various chronic illnesses and live in areas that already underserved. In New Mexico an innovative new model health care education delivery known as Project ECHO (Extension for Community Healthcare Outcomes) provides high-quality primary specialty a comparable population. Using state-of-the-art telehealth technology case-based learning, enables...

Recent works have cast some light on the mystery of why deep nets fit any data and generalize despite being very overparametrized. This paper analyzes training generalization for a simple 2-layer ReLU net with random initialization, provides following improvements over recent works: (i) Using tighter characterization speed than papers, an explanation neural labels leads to slower training, as originally observed in [Zhang et al. ICLR'17]. (ii) Generalization bound independent network size,...

We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our is an $n$ node multilayer neural net has degree at most $n^{\gamma}$ for some $\gamma <1$ each edge random weight $[-1,1]$. algorithm learns {\em almost all} networks this polynomial running time. The sample complexity quadratic or cubic depending upon details model. uses layerwise learning. It based novel idea observing correlations among features...

Background Project ECHO (Extension for Community Healthcare Outcomes) trains and mentors primary care providers (PCPs) in the of patients with complex conditions. is a distance education model that connects specialists numerous PCPs via simultaneous video link purpose facilitating case-based learning. This article describes teleECHO clinic based at University New Mexico Health Sciences Center focused on treatment substance use disorders (SUDs) behavioral health disorders. Methods Since 2005,...