IEEE Trans Pattern Anal Mach Intell - Negative Binomial Process Count and Mixture Modeling.

Tópicos

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{ import(1318) role(1303) understand(862) }
{ high(1669) rate(1365) level(1280) }
{ take(945) account(800) differ(722) }
{ model(2220) cell(1177) simul(1124) }
{ studi(1119) effect(1106) posit(819) }
{ measur(2081) correl(1212) valu(896) }
{ model(2656) set(1616) predict(1553) }
{ data(1737) use(1416) pattern(1282) }
{ network(2748) neural(1063) input(814) }
{ problem(2511) optim(1539) algorithm(950) }
{ compound(1573) activ(1297) structur(1058) }
{ group(2977) signific(1463) compar(1072) }
{ time(1939) patient(1703) rate(768) }
{ analysi(2126) use(1163) compon(1037) }
{ structur(1116) can(940) graph(676) }
{ cancer(2502) breast(956) screen(824) }
{ result(1111) use(1088) new(759) }
{ system(1976) rule(880) can(841) }
{ imag(1057) registr(996) error(939) }
{ imag(2830) propos(1344) filter(1198) }
{ treatment(1704) effect(941) patient(846) }
{ surgeri(1148) surgic(1085) robot(1054) }
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{ spatial(1525) area(1432) region(1030) }
{ health(3367) inform(1360) care(1135) }
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{ gene(2352) biolog(1181) express(1162) }
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Resumo

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to a NB process for count modeling. A draw from the NB process consists of a Poisson distributed finite number of distinct atoms, each of which is associated with a logarithmic distributed number of data samples. We reveal relationships between various count- and mixture-modeling distributions distributions, and construct a Poisson-logarithmic bivariate distribution that connects the NB and Chinese restaurant table distributions. Fundamental properties of the models are developed, and we derive efficient Bayesian inference. It is shown that with augmentation and normalization, the NB process and gamma-NB process can be reduced to the Dirichlet process and hierarchical Dirichlet process, respectively. These relationships highlight theoretical, structural and computational advantages of the NB process. A variety of NB processes, including the beta-geometric, beta-NB, marked-beta-NB, marked-gamma-NB and zero-inflated-NB processes, with distinct sharing mechanisms, are also constructed. These models are applied to topic modeling, with connections made to existing algorithms under Poisson factor analysis. Example results show the importance of inferring both the NB dispersion and probability parameters.

Resumo Limpo

seem disjoint problem count mixtur model unit negat binomi nb process gamma process employ model rate measur poisson process whose normal provid random probabl measur mixtur model whose margin lead nb process count model draw nb process consist poisson distribut finit number distinct atom associ logarithm distribut number data sampl reveal relationship various count mixturemodel distribut distribut construct poissonlogarithm bivari distribut connect nb chines restaur tabl distribut fundament properti model develop deriv effici bayesian infer shown augment normal nb process gammanb process can reduc dirichlet process hierarch dirichlet process respect relationship highlight theoret structur comput advantag nb process varieti nb process includ betageometr betanb markedbetanb markedgammanb zeroinflatednb process distinct share mechan also construct model appli topic model connect made exist algorithm poisson factor analysi exampl result show import infer nb dispers probabl paramet

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