ترغب بنشر مسار تعليمي؟ اضغط هنا

Diagnostics for Conditional Density Models and Bayesian Inference Algorithms

194   0   0.0 ( 0 )
 نشر من قبل David Zhao
 تاريخ النشر 2021
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

There has been growing interest in the AI community for precise uncertainty quantification. Conditional density models f(y|x), where x represents potentially high-dimensional features, are an integral part of uncertainty quantification in prediction and Bayesian inference. However, it is challenging to assess conditional density estimates and gain insight into modes of failure. While existing diagnostic tools can determine whether an approximated conditional density is compatible overall with a data sample, they lack a principled framework for identifying, locating, and interpreting the nature of statistically significant discrepancies over the entire feature space. In this paper, we present rigorous and easy-to-interpret diagnostics such as (i) the Local Coverage Test (LCT), which distinguishes an arbitrarily misspecified model from the true conditional density of the sample, and (ii) Amortized Local P-P plots (ALP) which can quickly provide interpretable graphical summaries of distributional differences at any location x in the feature space. Our validation procedures scale to high dimensions and can potentially adapt to any type of data at hand. We demonstrate the effectiveness of LCT and ALP through a simulated experiment and applications to prediction and parameter inference for image data.



قيم البحث

اقرأ أيضاً

We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet distributi ons, Negative binomial regression, Poisson-Gamma hierarchical models, Extreme value models, to name but a few. All of those models include a gamma function which does not admit a natural conjugate prior distribution providing a significant challenge to inference and prediction. To provide a data augmentation strategy, we construct and develop the theory of the class of Exponential Reciprocal Gamma distributions. This allows scalable EM and MCMC algorithms to be developed. We illustrate our methodology on a number of examples, including gamma shape inference, negative binomial regression and Dirichlet allocation. Finally, we conclude with directions for future research.
102 - Bokgyeong Kang , John Hughes , 2021
Models with intractable normalizing functions have numerous applications ranging from network models to image analysis to spatial point processes. Because the normalizing constants are functions of the parameters of interest, standard Markov chain Mo nte Carlo cannot be used for Bayesian inference for these models. A number of algorithms have been developed for such models. Some have the posterior distribution as the asymptotic distribution. Other asymptotically inexact algorithms do not possess this property. There is limited guidance for evaluating approximations based on these algorithms, and hence it is very hard to tune them. We propose two new diagnostics that address these problems for intractable normalizing function models. Our first diagnostic, inspired by the second Bartlett identity, applies in principle to any asymptotically exact or inexact algorithm. We develop an approximate version of this new diagnostic that is applicable to intractable normalizing function problems. Our second diagnostic is a Monte Carlo approximation to a kernel Stein discrepancy-based diagnostic introduced by Gorham and Mackey (2017). We provide theoretical justification for our methods. We apply our diagnostics to several algorithms in the context of challenging simulated and real data examples, including an Ising model, an exponential random graph model, and a Markov point process.
199 - Umberto Picchini 2012
Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard tool to mode l e.g. financial, neuronal and population growth dynamics. However inference for multidimensional SDE models is still very challenging, both computationally and theoretically. Approximate Bayesian computation (ABC) allow to perform Bayesian inference for models which are sufficiently complex that the likelihood function is either analytically unavailable or computationally prohibitive to evaluate. A computationally efficient ABC-MCMC algorithm is proposed, halving the running time in our simulations. Focus is on the case where the SDE describes latent dynamics in state-space models; however the methodology is not limited to the state-space framework. Simulation studies for a pharmacokinetics/pharmacodynamics model and for stochastic chemical reactions are considered and a MATLAB package implementing our ABC-MCMC algorithm is provided.
We develop a variational Bayesian (VB) approach for estimating large-scale dynamic network models in the network autoregression framework. The VB approach allows for the automatic identification of the dynamic structure of such a model and obtains a direct approximation of the posterior density. Compared to Markov Chain Monte Carlo (MCMC) based sampling approaches, the VB approach achieves enhanced computational efficiency without sacrificing estimation accuracy. In the simulation study conducted here, the proposed VB approach detects various types of proper active structures for dynamic network models. Compared to the alternative approach, the proposed method achieves similar or better accuracy, and its computational time is halved. In a real data analysis scenario of day-ahead natural gas flow prediction in the German gas transmission network with 51 nodes between October 2013 and September 2015, the VB approach delivers promising forecasting accuracy along with clearly detected structures in terms of dynamic dependence.
Nonparametric varying coefficient (NVC) models are useful for modeling time-varying effects on responses that are measured repeatedly. In this paper, we introduce the nonparametric varying coefficient spike-and-slab lasso (NVC-SSL) for Bayesian estim ation and variable selection in NVC models. The NVC-SSL simultaneously selects and estimates the significant varying coefficients, while also accounting for temporal correlations. Our model can be implemented using a computationally efficient expectation-maximization (EM) algorithm. We also employ a simple method to make our model robust to misspecification of the temporal correlation structure. In contrast to frequentist approaches, little is known about the large-sample properties for Bayesian NVC models when the dimension of the covariates $p$ grows much faster than sample size $n$. In this paper, we derive posterior contraction rates for the NVC-SSL model when $p gg n$ under both correct specification and misspecification of the temporal correlation structure. Thus, our results are derived under weaker assumptions than those seen in other high-dimensional NVC models which assume independent and identically distributed (iid) random errors. Finally, we illustrate our methodology through simulation studies and data analysis. Our method is implemented in the publicly available R package NVCSSL.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا