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Image information is restricted by the dynamic range of the detector, which can be addressed using multi-exposure image fusion (MEF). The conventional MEF approach employed in ptychography is often inadequate under conditions of low signal-to-noise ratio (SNR) or variations in illumination intensity. To address this, we developed a Bayesian approach for MEF based on a modified Poisson noise model that considers the background and saturation. Our method outperforms conventional MEF under challenging experimental conditions, as demonstrated by the synthetic and experimental data. Furthermore, this method is versatile and applicable to any imaging scheme requiring high dynamic range (HDR).

Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI methods have made use of neural networks (NN) to provide approximate, yet expressive constructs for the unavailable likelihood function and the posterior distribution. However, they do not generally achieve an optimal trade-off between accuracy and computational demand. In this work, we propose an alternative that provides both approximations to the likelihood and the posterior distribution, using structured mixtures of probability distributions. Our approach produces accurate posterior inference when compared to state-of-the-art NN-based SBI methods, while exhibiting a much smaller computational footprint. We illustrate our results on several benchmark models from the SBI literature.

The Fisher-Rao distance between two probability distributions of a statistical model is defined as the Riemannian geodesic distance induced by the Fisher information metric. In order to calculate the Fisher-Rao distance in closed-form, we need (1) to elicit a formula for the Fisher-Rao geodesics, and (2) to integrate the Fisher length element along those geodesics. We consider several numerically robust approximation and bounding techniques for the Fisher-Rao distances: First, we report generic upper bounds on Fisher-Rao distances based on closed-form 1D Fisher-Rao distances of submodels. Second, we describe several generic approximation schemes depending on whether the Fisher-Rao geodesics or pregeodesics are available in closed-form or not. In particular, we obtain a generic method to guarantee an arbitrarily small additive error on the approximation provided that Fisher-Rao pregeodesics and tight lower and upper bounds are available. Third, we consider the case of Fisher metrics being Hessian metrics, and report generic tight upper bounds on the Fisher-Rao distances using techniques of information geometry. Uniparametric and biparametric statistical models always have Fisher Hessian metrics, and in general a simple test allows to check whether the Fisher information matrix yields a Hessian metric or not. Fourth, we consider elliptical distribution families and show how to apply the above techniques to these models. We also propose two new distances based either on the Fisher-Rao lengths of curves serving as proxies of Fisher-Rao geodesics, or based on the Birkhoff/Hilbert projective cone distance. Last, we consider an alternative group-theoretic approach for statistical transformation models based on the notion of maximal invariant which yields insights on the structures of the Fisher-Rao distance formula which may be used fruitfully in applications.

We solve constrained optimal transport problems between the laws of solutions of stochastic differential equations (SDEs). We consider SDEs with irregular coefficients, making only minimal regularity assumptions. We show that the so-called synchronous coupling is optimal among bicausal couplings, that is couplings that respect the flow of information encoded in the stochastic processes. Our results provide a method to numerically compute the adapted Wasserstein distance between laws of SDEs with irregular coefficients. Moreover, we introduce a transformation-based semi-implicit numerical scheme and establish the first strong convergence result for SDEs with exponentially growing and discontinuous drift.

Regression models that incorporate smooth functions of predictor variables to explain the relationships with a response variable have gained widespread usage and proved successful in various applications. By incorporating smooth functions of predictor variables, these models can capture complex relationships between the response and predictors while still allowing for interpretation of the results. In situations where the relationships between a response variable and predictors are explored, it is not uncommon to assume that these relationships adhere to certain shape constraints. Examples of such constraints include monotonicity and convexity. The scam package for R has become a popular package to carry out the full fitting of exponential family generalized additive modelling with shape restrictions on smooths. The paper aims to extend the existing framework of shape-constrained generalized additive models (SCAM) to accommodate smooth interactions of covariates, linear functionals of shape-constrained smooths and incorporation of residual autocorrelation. The methods described in this paper are implemented in the recent version of the package scam, available on the Comprehensive R Archive Network (CRAN).

We present a comprehensive analysis of singular vector and singular subspace perturbations in the context of the signal plus random Gaussian noise matrix model. Assuming a low-rank signal matrix, we extend the Wedin-Davis-Kahan theorem in a fully generalized manner, applicable to any unitarily invariant matrix norm, extending previous results of O'Rourke, Vu and the author. We also obtain the fine-grained results, which encompass the $\ell_\infty$ analysis of singular vectors, the $\ell_{2, \infty}$ analysis of singular subspaces, as well as the exploration of linear and bilinear functions related to the singular vectors. Moreover, we explore the practical implications of these findings, in the context of the Gaussian mixture model and the submatrix localization problem.

We propose an implicit Discontinuous Galerkin (DG) discretization for incompressible two-phase flows using an artificial compressibility formulation. The conservative level set (CLS) method is employed in combination with a reinitialization procedure to capture the moving interface. A projection method based on the L-stable TR-BDF2 method is adopted for the time discretization of the Navier-Stokes equations and of the level set method. Adaptive Mesh Refinement (AMR) is employed to enhance the resolution in correspondence of the interface between the two fluids. The effectiveness of the proposed approach is shown in a number of classical benchmarks. A specific analysis on the influence of different choices of the mixture viscosity is also carried out.

A model is considered well-calibrated when its probability estimate aligns with the actual likelihood of the output being correct. Calibrating language models (LMs) is crucial, as it plays a vital role in detecting and mitigating hallucinations of LMs as well as building more trustworthy models. However, standard calibration techniques may not be suited for LM calibration. For instance, post-processing methods such as temperature scaling do not reorder the candidate generations. On the other hand, training-based methods require fine-tuning the entire model, which is impractical for LMs of large scale. We present LitCab, a lightweight calibration mechanism consisting of a single linear layer that takes the input text representation and predicts a bias term, which is then added to the LM output logits. LitCab improves model calibration by only adding < 2% of the original model parameters. For evaluation, we construct CaT, a benchmark consisting of eight text generation tasks, covering responses ranging from short phrases to paragraphs. We test LitCab with Llama2-7B, where it improves calibration across all tasks, reducing the average ECE score by as large as 30%. We further conduct a comprehensive evaluation with multiple popular open-sourced LMs from GPT and LLaMA families, yielding the following key findings: (i) Larger models within the same family exhibit better calibration on tasks with short generation tasks, but not necessarily for longer ones. (ii) GPT-family models show superior calibration compared to LLaMA, Llama2, and Vicuna models, despite having much fewer parameters. (iii) Fine-tuning pretrained model (e.g., LLaMA) with samples of limited purpose (e.g., conversations) may lead to worse calibration, highlighting the importance of fine-tuning setups for calibrating LMs.

Conventional entity typing approaches are based on independent classification paradigms, which make them difficult to recognize inter-dependent, long-tailed and fine-grained entity types. In this paper, we argue that the implicitly entailed extrinsic and intrinsic dependencies between labels can provide critical knowledge to tackle the above challenges. To this end, we propose \emph{Label Reasoning Network(LRN)}, which sequentially reasons fine-grained entity labels by discovering and exploiting label dependencies knowledge entailed in the data. Specifically, LRN utilizes an auto-regressive network to conduct deductive reasoning and a bipartite attribute graph to conduct inductive reasoning between labels, which can effectively model, learn and reason complex label dependencies in a sequence-to-set, end-to-end manner. Experiments show that LRN achieves the state-of-the-art performance on standard ultra fine-grained entity typing benchmarks, and can also resolve the long tail label problem effectively.