Accurately modeling the production of new ideas is crucial for innovation theory and endogenous growth models. This paper provides a comprehensive methodological survey of strategies for estimating idea production functions. We explore various methods, including naive approaches, linear regression, maximum likelihood estimation, and Bayesian inference, each suited to different data availability settings. Through case studies ranging from total factor productivity to software R&D, we show how to apply these methodologies in practice. Our synthesis provides researchers with guidance on strategies for characterizing idea production functions and highlights obstacles that must be addressed through further empirical validation.
In this letter, we investigate a new generalized double Pareto based on off-grid sparse Bayesian learning (GDPOGSBL) approach to improve the performance of direction of arrival (DOA) estimation in underdetermined scenarios. The method aims to enhance the sparsity of source signal by utilizing the generalized double Pareto (GDP) prior. Firstly, we employ a first-order linear Taylor expansion to model the real array manifold matrix, and Bayesian inference is utilized to calculate the off-grid error, which mitigates the grid dictionary mismatch problem in underdetermined scenarios. Secondly, an innovative grid refinement method is introduced, treating grid points as iterative parameters to minimize the modeling error between the source and grid points. The numerical simulation results verify the superiority of the proposed strategy, especially when dealing with a coarse grid and few snapshots.
We advocate for a new paradigm of cosmological likelihood-based inference, leveraging recent developments in machine learning and its underlying technology, to accelerate Bayesian inference in high-dimensional settings. Specifically, we combine (i) emulation, where a machine learning model is trained to mimic cosmological observables, e.g. CosmoPower-JAX; (ii) differentiable and probabilistic programming, e.g. JAX and NumPyro, respectively; (iii) scalable Markov chain Monte Carlo (MCMC) sampling techniques that exploit gradients, e.g. Hamiltonian Monte Carlo; and (iv) decoupled and scalable Bayesian model selection techniques that compute the Bayesian evidence purely from posterior samples, e.g. the learned harmonic mean implemented in harmonic. This paradigm allows us to carry out a complete Bayesian analysis, including both parameter estimation and model selection, in a fraction of the time of traditional approaches. First, we demonstrate the application of this paradigm on a simulated cosmic shear analysis for a Stage IV survey in 37- and 39-dimensional parameter spaces, comparing $\Lambda$CDM and a dynamical dark energy model ($w_0w_a$CDM). We recover posterior contours and evidence estimates that are in excellent agreement with those computed by the traditional nested sampling approach while reducing the computational cost from 8 months on 48 CPU cores to 2 days on 12 GPUs. Second, we consider a joint analysis between three simulated next-generation surveys, each performing a 3x2pt analysis, resulting in 157- and 159-dimensional parameter spaces. Standard nested sampling techniques are simply unlikely to be feasible in this high-dimensional setting, requiring a projected 12 years of compute time on 48 CPU cores; on the other hand, the proposed approach only requires 8 days of compute time on 24 GPUs. All packages used in our analyses are publicly available.
This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian inference often substitute computationally expensive high-fidelity models with machine learning models, thereby introducing approximation errors, our approach offers a computationally efficient alternative by augmenting high-fidelity models with low-fidelity ones within a hierarchical framework. The multilevel approach utilizes the low-fidelity machine learning model (MLM) for inexpensive evaluation of proposed samples thereby improving the acceptance of samples by the high-fidelity model. The hierarchy in our multilevel algorithm is derived from geometric multigrid hierarchy. We utilize an MLM to acclerate the coarse level sampling. Training machine learning model for the coarsest level significantly reduces the computational cost associated with generating training data and training the model. We present an MCMC algorithm to accelerate the coarsest level sampling using MLM and account for the approximation error introduced. We provide theoretical proofs of detailed balance and demonstrate that our multilevel approach constitutes a consistent MCMC algorithm. Additionally, we derive conditions on the accuracy of the machine learning model to facilitate more efficient hierarchical sampling. Our technique is demonstrated on a standard benchmark inference problem in groundwater flow, where we estimate the probability density of a quantity of interest using a four-level MCMC algorithm. Our proposed algorithm accelerates multilevel sampling by a factor of two while achieving similar accuracy compared to sampling using the standard multilevel algorithm.
Facing the current debate on whether Large Language Models (LLMs) attain near-human intelligence levels (Mitchell & Krakauer, 2023; Bubeck et al., 2023; Kosinski, 2023; Shiffrin & Mitchell, 2023; Ullman, 2023), the current study introduces a benchmark for evaluating social intelligence, one of the most distinctive aspects of human cognition. We developed a comprehensive theoretical framework for social dynamics and introduced two evaluation tasks: Inverse Reasoning (IR) and Inverse Inverse Planning (IIP). Our approach also encompassed a computational model based on recursive Bayesian inference, adept at elucidating diverse human behavioral patterns. Extensive experiments and detailed analyses revealed that humans surpassed the latest GPT models in overall performance, zero-shot learning, one-shot generalization, and adaptability to multi-modalities. Notably, GPT models demonstrated social intelligence only at the most basic order (order = 0), in stark contrast to human social intelligence (order >= 2). Further examination indicated a propensity of LLMs to rely on pattern recognition for shortcuts, casting doubt on their possession of authentic human-level social intelligence. Our codes, dataset, appendix and human data are released at https://github.com/bigai-ai/Evaluate-n-Model-Social-Intelligence.
Prediction-powered inference (PPI) is a method that improves statistical estimates based on limited human-labeled data. Specifically, PPI methods provide tighter confidence intervals by combining small amounts of human-labeled data with larger amounts of data labeled by a reasonably accurate, but potentially biased, automatic system. We propose a framework for PPI based on Bayesian inference that allows researchers to develop new task-appropriate PPI methods easily. Exploiting the ease with which we can design new metrics, we propose improved PPI methods for several importantcases, such as autoraters that give discrete responses (e.g., prompted LLM ``judges'') and autoraters with scores that have a non-linear relationship to human scores.
We investigate a joint visibility region (VR) detection and channel estimation problem in extremely large-scale multiple-input-multiple-output (XL-MIMO) systems, where near-field propagation and spatial non-stationary effects exist. In this case, each scatterer can only see a subset of antennas, i.e., it has a certain VR over the antennas. Because of the spatial correlation among adjacent sub-arrays, VR of scatterers exhibits a two-dimensional (2D) clustered sparsity. We design a 2D Markov prior model to capture such a structured sparsity. Based on this, a novel alternating maximum a posteriori (MAP) framework is developed for high-accuracy VR detection and channel estimation. The alternating MAP framework consists of three basic modules: a channel estimation module, a VR detection module, and a grid update module. Specifically, the first module is a low-complexity inverse-free variational Bayesian inference (IF-VBI) algorithm that avoids the matrix inverse via minimizing a relaxed Kullback-Leibler (KL) divergence. The second module is a structured expectation propagation (EP) algorithm which has the ability to deal with complicated prior information. And the third module refines polar-domain grid parameters via gradient ascent. Simulations demonstrate the superiority of the proposed algorithm in both VR detection and channel estimation.
We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks.
Vertical federated learning (VFL) has emerged as a paradigm for collaborative model estimation across multiple clients, each holding a distinct set of covariates. This paper introduces the first comprehensive framework for fitting Bayesian models in the VFL setting. We propose a novel approach that leverages data augmentation techniques to transform VFL problems into a form compatible with existing Bayesian federated learning algorithms. We present an innovative model formulation for specific VFL scenarios where the joint likelihood factorizes into a product of client-specific likelihoods. To mitigate the dimensionality challenge posed by data augmentation, which scales with the number of observations and clients, we develop a factorized amortized variational approximation that achieves scalability independent of the number of observations. We showcase the efficacy of our framework through extensive numerical experiments on logistic regression, multilevel regression, and a novel hierarchical Bayesian split neural net model. Our work paves the way for privacy-preserving, decentralized Bayesian inference in vertically partitioned data scenarios, opening up new avenues for research and applications in various domains.
Fine-tuned Large Language Models (LLMs) often suffer from overconfidence and poor calibration, particularly when fine-tuned on small datasets. To address these challenges, we propose a simple combination of Low-Rank Adaptation (LoRA) with Gaussian Stochastic Weight Averaging (SWAG), facilitating approximate Bayesian inference in LLMs. Through extensive testing across several Natural Language Processing (NLP) benchmarks, we demonstrate that our straightforward and computationally efficient approach improves model generalization and calibration competitively with comparable, more sophisticated methods for Bayesian inference in LLMs. We further show that our method exhibits greater robustness against distribution shift, as reflected in its improved performance on out-of-distribution tasks.
In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a robust framework for extracting theoretical insights from observational data. However, its computational demands can be substantial, primarily due to the need for numerous likelihood function evaluations. Our proposed method utilizes the power of deep learning, employing feedforward neural networks to approximate the likelihood function dynamically during the Bayesian inference process. Unlike traditional approaches, our method trains neural networks on-the-fly using the current set of live points as training data, without the need for pre-training. This flexibility enables adaptation to various theoretical models and datasets. We perform simple hyperparameter optimization using genetic algorithms to suggest initial neural network architectures for learning each likelihood function. Once sufficient accuracy is achieved, the neural network replaces the original likelihood function. The implementation integrates with nested sampling algorithms and has been thoroughly evaluated using both simple cosmological dark energy models and diverse observational datasets. Additionally, we explore the potential of genetic algorithms for generating initial live points within nested sampling inference, opening up new avenues for enhancing the efficiency and effectiveness of Bayesian inference methods.
To support mechanism online learning and facilitate digital twin development for biomanufacturing processes, this paper develops an efficient Bayesian inference approach for partially observed enzymatic stochastic reaction network (SRN), a fundamental building block of multi-scale bioprocess mechanistic model. To tackle the critical challenges brought by the nonlinear stochastic differential equations (SDEs)-based mechanistic model with partially observed state and having measurement errors, an interpretable Bayesian updating linear noise approximation (LNA) metamodel, incorporating the structure information of the mechanistic model, is proposed to approximate the likelihood of observations. Then, an efficient posterior sampling approach is developed by utilizing the gradients of the derived likelihood to speed up the convergence of Markov Chain Monte Carlo (MCMC). The empirical study demonstrates that the proposed approach has a promising performance.
Large Language Models (LLMs) are trained on massive text corpora, which are encoded with diverse personality traits. This triggers an interesting goal of eliciting a desired personality trait from the LLM, and probing its behavioral preferences. Accordingly, we formalize the persona elicitation task, aiming to customize LLM behaviors to align with a target persona. We present Persona In-Context Learning (PICLe), a novel persona elicitation framework grounded in Bayesian inference. At the core, PICLe introduces a new ICL example selection criterion based on likelihood ratio, which is designed to optimally guide the model in eliciting a specific target persona. We demonstrate the effectiveness of PICLe through extensive comparisons against baseline methods across three contemporary LLMs. Code is available at https://github.com/deeplearning-wisc/picle.
Likelihood-free inference methods based on neural conditional density estimation were shown to drastically reduce the simulation burden in comparison to classical methods such as ABC. When applied in the context of any latent variable model, such as a Hidden Markov model (HMM), these methods are designed to only estimate the parameters, rather than the joint distribution of the parameters and the hidden states. Naive application of these methods to a HMM, ignoring the inference of this joint posterior distribution, will thus produce an inaccurate estimate of the posterior predictive distribution, in turn hampering the assessment of goodness-of-fit. To rectify this problem, we propose a novel, sample-efficient likelihood-free method for estimating the high-dimensional hidden states of an implicit HMM. Our approach relies on learning directly the intractable posterior distribution of the hidden states, using an autoregressive-flow, by exploiting the Markov property. Upon evaluating our approach on some implicit HMMs, we found that the quality of the estimates retrieved using our method is comparable to what can be achieved using a much more computationally expensive SMC algorithm.
When querying a large language model (LLM), the context, i.e. personal, demographic, and cultural information specific to an end-user, can significantly shape the response of the LLM. For example, asking the model to explain Newton's second law with the context "I am a toddler" yields a different answer compared to the context "I am a physics professor." Proper usage of the context enables the LLM to generate personalized responses, whereas inappropriate contextual influence can lead to stereotypical and potentially harmful generations (e.g. associating "female" with "housekeeper"). In practice, striking the right balance when leveraging context is a nuanced and challenging problem that is often situation-dependent. One common approach to address this challenge is to fine-tune LLMs on contextually appropriate responses. However, this approach is expensive, time-consuming, and not controllable for end-users in different situations. In this work, we propose Context Steering (CoS) - a simple training-free method that can be easily applied to autoregressive LLMs at inference time. By measuring the contextual influence in terms of token prediction likelihood and modulating it, our method enables practitioners to determine the appropriate level of contextual influence based on their specific use case and end-user base. We showcase a variety of applications of CoS including amplifying the contextual influence to achieve better personalization and mitigating unwanted influence for reducing model bias. In addition, we show that we can combine CoS with Bayesian Inference to quantify the extent of hate speech on the internet. We demonstrate the effectiveness of CoS on state-of-the-art LLMs and benchmarks.
A fundamental problem associated with the task of network reconstruction from dynamical or behavioral data consists in determining the most appropriate model complexity in a manner that prevents overfitting, and produces an inferred network with a statistically justifiable number of edges. The status quo in this context is based on $L_{1}$ regularization combined with cross-validation. However, besides its high computational cost, this commonplace approach unnecessarily ties the promotion of sparsity with weight "shrinkage". This combination forces a trade-off between the bias introduced by shrinkage and the network sparsity, which often results in substantial overfitting even after cross-validation. In this work, we propose an alternative nonparametric regularization scheme based on hierarchical Bayesian inference and weight quantization, which does not rely on weight shrinkage to promote sparsity. Our approach follows the minimum description length (MDL) principle, and uncovers the weight distribution that allows for the most compression of the data, thus avoiding overfitting without requiring cross-validation. The latter property renders our approach substantially faster to employ, as it requires a single fit to the complete data. As a result, we have a principled and efficient inference scheme that can be used with a large variety of generative models, without requiring the number of edges to be known in advance. We also demonstrate that our scheme yields systematically increased accuracy in the reconstruction of both artificial and empirical networks. We highlight the use of our method with the reconstruction of interaction networks between microbial communities from large-scale abundance samples involving in the order of $10^{4}$ to $10^{5}$ species, and demonstrate how the inferred model can be used to predict the outcome of interventions in the system.
Deep generative models have been accelerating the inverse design process in material and drug design. Unlike their counterpart property predictors in typical molecular design frameworks, generative molecular design models have seen fewer efforts on uncertainty quantification (UQ) due to computational challenges in Bayesian inference posed by their large number of parameters. In this work, we focus on the junction-tree variational autoencoder (JT-VAE), a popular model for generative molecular design, and address this issue by leveraging the low dimensional active subspace to capture the uncertainty in the model parameters. Specifically, we approximate the posterior distribution over the active subspace parameters to estimate the epistemic model uncertainty in an extremely high dimensional parameter space. The proposed UQ scheme does not require alteration of the model architecture, making it readily applicable to any pre-trained model. Our experiments demonstrate the efficacy of the AS-based UQ and its potential impact on molecular optimization by exploring the model diversity under epistemic uncertainty.
Prediction of road users' behaviors in the context of autonomous driving has gained considerable attention by the scientific community in the last years. Most works focus on predicting behaviors based on kinematic information alone, a simplification of the reality since road users are humans, and as such they are highly influenced by their surrounding context. In addition, a large plethora of research works rely on powerful Deep Learning techniques, which exhibit high performance metrics in prediction tasks but may lack the ability to fully understand and exploit the contextual semantic information contained in the road scene, not to mention their inability to provide explainable predictions that can be understood by humans. In this work, we propose an explainable road users' behavior prediction system that integrates the reasoning abilities of Knowledge Graphs (KG) and the expressiveness capabilities of Large Language Models (LLM) by using Retrieval Augmented Generation (RAG) techniques. For that purpose, Knowledge Graph Embeddings (KGE) and Bayesian inference are combined to allow the deployment of a fully inductive reasoning system that enables the issuing of predictions that rely on legacy information contained in the graph as well as on current evidence gathered in real time by onboard sensors. Two use cases have been implemented following the proposed approach: 1) Prediction of pedestrians' crossing actions; 2) Prediction of lane change maneuvers. In both cases, the performance attained surpasses the current state of the art in terms of anticipation and F1-score, showing a promising avenue for future research in this field.
Large neural networks trained on large datasets have become the dominant paradigm in machine learning. These systems rely on maximum likelihood point estimates of their parameters, precluding them from expressing model uncertainty. This may result in overconfident predictions and it prevents the use of deep learning models for sequential decision making. This thesis develops scalable methods to equip neural networks with model uncertainty. In particular, we leverage the linearised Laplace approximation to equip pre-trained neural networks with the uncertainty estimates provided by their tangent linear models. This turns the problem of Bayesian inference in neural networks into one of Bayesian inference in conjugate Gaussian-linear models. Alas, the cost of this remains cubic in either the number of network parameters or in the number of observations times output dimensions. By assumption, neither are tractable. We address this intractability by using stochastic gradient descent (SGD) -- the workhorse algorithm of deep learning -- to perform posterior sampling in linear models and their convex duals: Gaussian processes. With this, we turn back to linearised neural networks, finding the linearised Laplace approximation to present a number of incompatibilities with modern deep learning practices -- namely, stochastic optimisation, early stopping and normalisation layers -- when used for hyperparameter learning. We resolve these and construct a sample-based EM algorithm for scalable hyperparameter learning with linearised neural networks. We apply the above methods to perform linearised neural network inference with ResNet-50 (25M parameters) trained on Imagenet (1.2M observations and 1000 output dimensions). Additionally, we apply our methods to estimate uncertainty for 3d tomographic reconstructions obtained with the deep image prior network.
Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn latent representations in modern multivariate data sets with complex dependency structures. Among these, the exponential family graphical models are especially popular, given their fairly well-understood statistical properties and computational scalability to high-dimensional data based on pseudo-likelihood methods. These models have been successfully applied in many fields, such as the Ising model in statistical physics and count graphical models in genomics. Another strand of models allows some nodes to be latent, so as to allow the marginal distribution of the observable nodes to depart from exponential family to capture more complex dependence. These approaches form the basis of generative models in artificial intelligence, such as the Boltzmann machines and their restricted versions. A fundamental barrier to likelihood-based (i.e., both maximum likelihood and fully Bayesian) inference in both fully and partially observed cases is the intractability of the likelihood. The usual workaround is via adopting pseudo-likelihood based approaches, following the pioneering work of Besag (1974). The goal of this paper is to demonstrate that full likelihood based analysis of these models is feasible in a computationally efficient manner. The chief innovation lies in using a technique of Geyer (1991) utilizing the tractable independence model underlying an intractable graphical model, to estimate the normalizing constant, as well as its gradient. Extensive numerical results, supporting theory and comparisons with pseudo-likelihood based approaches demonstrate the applicability of the proposed method.