In this work we continue studies of the uncertainty quantification problem in emission tomographies such as PET or SPECT. In particular, we consider a scenario when additional multimodal data (e.g., anatomical MRI images) are available. To solve the aforementioned problem we adapt the recently proposed nonparametric posterior learning technique to the context of Poisson-type data in emission tomography. Using this approach we derive sampling algorithms which are trivially parallelizable, scalable and very easy to implement. In addition, we prove conditional consistency and tightness for the distribution of produced samples in the small noise limit (i.e., when the acquisition time tends to infinity) and derive new geometrical and necessary condition on how MRI images must be used. This condition arises naturally in the context of misspecified generalized Poisson models. We also contrast our approach with bayesian MCMC sampling based one one data augmentation scheme which is very popular in the context of EM-type algorithms for PET or SPECT. We show theoretically and also numerically that such data augmentation significantly increases mixing times for the Markov chain. In view of this, our algorithms seem to give a reasonable trade-off between design complexity, scalability, numerical load and asessement for the uncertainty quantification.

Naive, Yet it is one of the very simple yet powerful and easy to implement algorithm used in Supervised learning mainly for classification problems. Through this blog, I intend to make y'all have a basic understanding of the Naive Bayes classifier and its applications and why is it called naive. Naive Bayes classifier is built upon three main fundamental theories which are Probababilty, Conditional Probability and Bayes theorem. I assume that my readers have knowledge of these if not you can find my blog on these over here. I will just try to give an overview of what is Baye's theorem because that is important to understand Naive Baye's theorem.

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications of such models, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a noisy tensor. Hence, understanding the fundamental limits and the attainable performance of estimators of that signal inevitably calls for the study of random tensors. Substantial progress has been achieved on this subject thanks to recent efforts, under the assumption that the tensor dimensions grow large. Yet, some of the most significant among these results--in particular, a precise characterization of the abrupt phase transition (in terms of signal-to-noise ratio) that governs the performance of the maximum likelihood (ML) estimator of a symmetric rank-one model with Gaussian noise--were derived on the basis of statistical physics ideas, which are not easily accessible to non-experts. In this work, we develop a sharply distinct approach, relying instead on standard but powerful tools brought by years of advances in random matrix theory. The key idea is to study the spectra of random matrices arising from contractions of a given random tensor. We show how this gives access to spectral properties of the random tensor itself. In the specific case of a symmetric rank-one model with Gaussian noise, our technique yields a hitherto unknown characterization of the local maximum of the ML problem that is global above the phase transition threshold. This characterization is in terms of a fixed-point equation satisfied by a formula that had only been previously obtained via statistical physics methods. Moreover, our analysis sheds light on certain properties of the landscape of the ML problem in the large-dimensional setting. Our approach is versatile and can be extended to other models, such as asymmetric, non-Gaussian and higher-order ones.

This survey gives an overview of Monte Carlo methodologies using surrogate models, for dealing with densities which are intractable, costly, and/or noisy. This type of problem can be found in numerous real-world scenarios, including stochastic optimization and reinforcement learning, where each evaluation of a density function may incur some computationally-expensive or even physical (real-world activity) cost, likely to give different results each time. The surrogate model does not incur this cost, but there are important trade-offs and considerations involved in the choice and design of such methodologies. We classify the different methodologies into three main classes and describe specific instances of algorithms under a unified notation. A modular scheme which encompasses the considered methods is also presented. A range of application scenarios is discussed, with special attention to the likelihood-free setting and reinforcement learning. Several numerical comparisons are also provided.

Autonomous systems often operate in environments where the behavior of multiple agents is coordinated by a shared global state. Reliable estimation of the global state is thus critical for successfully operating in a multi-agent setting. We introduce agent-aware state estimation -- a framework for calculating indirect estimations of state given observations of the behavior of other agents in the environment. We also introduce transition-independent agent-aware state estimation -- a tractable class of agent-aware state estimation -- and show that it allows the speed of inference to scale linearly with the number of agents in the environment. As an example, we model traffic light classification in instances of complete loss of direct observation. By taking into account observations of vehicular behavior from multiple directions of traffic, our approach exhibits accuracy higher than that of existing traffic light-only HMM methods on a real-world autonomous vehicle data set under a variety of simulated occlusion scenarios.

Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for machine learning models. They cause significant gaps between model performance in the lab and in the real world. Our work is a solution to prevalence bias. Prevalence bias is the discrepancy between the prevalence of a pathology and its sampling rate in the training dataset, introduced upon collecting data or due to the practioner rebalancing the training batches. This paper lays the theoretical and computational framework for training models, and for prediction, in the presence of prevalence bias. Concretely a bias-corrected loss function, as well as bias-corrected predictive rules, are derived under the principles of Bayesian risk minimization. The loss exhibits a direct connection to the information gain. It offers a principled alternative to heuristic training losses and complements test-time procedures based on selecting an operating point from summary curves. It integrates seamlessly in the current paradigm of (deep) learning using stochastic backpropagation and naturally with Bayesian models.

Microorganisms are widely distributed in the human daily living environment. They play an essential role in environmental pollution control, disease prevention and treatment, and food and drug production. The identification, counting, and detection are the basic steps for making full use of different microorganisms. However, the conventional analysis methods are expensive, laborious, and time-consuming. To overcome these limitations, artificial neural networks are applied for microorganism image analysis. We conduct this review to understand the development process of microorganism image analysis based on artificial neural networks. In this review, the background and motivation are introduced first. Then, the development of artificial neural networks and representative networks are introduced. After that, the papers related to microorganism image analysis based on classical and deep neural networks are reviewed from the perspectives of different tasks. In the end, the methodology analysis and potential direction are discussed.

We investigate active learning in Gaussian Process state-space models (GPSSM). Our problem is to actively steer the system through latent states by determining its inputs such that the underlying dynamics can be optimally learned by a GPSSM. In order that the most informative inputs are selected, we employ mutual information as our active learning criterion. In particular, we present two approaches for the approximation of mutual information for the GPSSM given latent states. The proposed approaches are evaluated in several physical systems where we actively learn the underlying non-linear dynamics represented by the state-space model.

Particle-based approximate Bayesian inference approaches such as Stein Variational Gradient Descent (SVGD) combine the flexibility and convergence guarantees of sampling methods with the computational benefits of variational inference. In practice, SVGD relies on the choice of an appropriate kernel function, which impacts its ability to model the target distribution -- a challenging problem with only heuristic solutions. We propose Neural Variational Gradient Descent (NVGD), which is based on parameterizing the witness function of the Stein discrepancy by a deep neural network whose parameters are learned in parallel to the inference, mitigating the necessity to make any kernel choices whatsoever. We empirically evaluate our method on popular synthetic inference problems, real-world Bayesian linear regression, and Bayesian neural network inference.

We propose a models with lower latency and power consumption while Bayesian approach to trend detection in which also ensuring privacy. However, as there is no access to the probability of a keyword being trendy, given actual data from participating devices, it poses a problem a dataset, is computed via Bayes' Theorem; the for the analysis of federated learning models. Federated analytics probability of a dataset, given that a keyword (Ramage & Mazzocchi) is a practice introduced to is trendy, is computed through secure aggregation solve this problem. It uses the same infrastructure as federated of such conditional probabilities over local learning to aggregate the computed metric by each datasets of users. We propose a protocol, named participating device using local data and shared models. SAFE, for Bayesian federated analytics that offers Federated analytics has already gone beyond just measuring sufficient privacy for production-grade use the quality metric to computing descriptive statistics cases and reduces the computational burden of (Ramage & Mazzocchi; Zhu et al., 2020), generating synthetic users and an aggregator. We illustrate this approach data (Xin et al., 2020; Chaulwar, 2020) and learning with a trend detection experiment and discuss new insights (Chen et al., 2019). These methods are generally how this approach could be extended further combined with secure aggregation protocols to ensure to make it production-ready.