Federated Learning (FL) emerges as a distributed machine learning paradigm without end-user data transmission, effectively avoiding privacy leakage. Participating devices in FL are usually bandwidth-constrained, and the uplink is much slower than the downlink in wireless networks, which causes a severe uplink communication bottleneck. A prominent direction to alleviate this problem is federated dropout, which drops fractional weights of local models. However, existing federated dropout studies focus on random or ordered dropout and lack theoretical support, resulting in unguaranteed performance. In this paper, we propose Federated learning with Bayesian Inference-based Adaptive Dropout (FedBIAD), which regards weight rows of local models as probability distributions and adaptively drops partial weight rows based on importance indicators correlated with the trend of local training loss. By applying FedBIAD, each client adaptively selects a high-quality dropping pattern with accurate approximations and only transmits parameters of non-dropped weight rows to mitigate uplink costs while improving accuracy. Theoretical analysis demonstrates that the convergence rate of the average generalization error of FedBIAD is minimax optimal up to a squared logarithmic factor. Extensive experiments on image classification and next-word prediction show that compared with status quo approaches, FedBIAD provides 2x uplink reduction with an accuracy increase of up to 2.41% even on non-Independent and Identically Distributed (non-IID) data, which brings up to 72% decrease in training time.
The number of modes in a probability density function is representative of the complexity of a model and can also be viewed as the number of subpopulations. Despite its relevance, there has been limited research in this area. A novel approach to estimating the number of modes in the univariate setting is presented, focusing on prediction accuracy and inspired by some overlooked aspects of the problem: the need for structure in the solutions, the subjective and uncertain nature of modes, and the convenience of a holistic view that blends local and global density properties. The technique combines flexible kernel estimators and parsimonious compositional splines in the Bayesian inference paradigm, providing soft solutions and incorporating expert judgment. The procedure includes feature exploration, model selection, and mode testing, illustrated in a sports analytics case study showcasing multiple companion visualisation tools. A thorough simulation study also demonstrates that traditional modality-driven approaches paradoxically struggle to provide accurate results. In this context, the new method emerges as a top-tier alternative, offering innovative solutions for analysts.
Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a transport map that pushes forward a simple reference (e.g., a standard Gaussian) to a target distribution. While these approaches successfully describe many non-Gaussian problems, their performance is often limited by parametric bias and the reliability of gradient-based (adversarial) optimizers to learn these transformations. This work proposes a non-parametric generative model that iteratively maps reference samples to the target. The model uses block-triangular transport maps, whose components are shown to characterize conditionals of the target distribution. These maps arise from solving an optimal transport problem with a weighted $L^2$ cost function, thereby extending the data-driven approach in [Trigila and Tabak, 2016] for conditional sampling. The proposed approach is demonstrated on a two dimensional example and on a parameter inference problem involving nonlinear ODEs.
Contemporary scientific research is a distributed, collaborative endeavor, carried out by teams of researchers, regulatory institutions, funding agencies, commercial partners, and scientific bodies, all interacting with each other and facing different incentives. To maintain scientific rigor, statistical methods should acknowledge this state of affairs. To this end, we study hypothesis testing when there is an agent (e.g., a researcher or a pharmaceutical company) with a private prior about an unknown parameter and a principal (e.g., a policymaker or regulator) who wishes to make decisions based on the parameter value. The agent chooses whether to run a statistical trial based on their private prior and then the result of the trial is used by the principal to reach a decision. We show how the principal can conduct statistical inference that leverages the information that is revealed by an agent's strategic behavior -- their choice to run a trial or not. In particular, we show how the principal can design a policy to elucidate partial information about the agent's private prior beliefs and use this to control the posterior probability of the null. One implication is a simple guideline for the choice of significance threshold in clinical trials: the type-I error level should be set to be strictly less than the cost of the trial divided by the firm's profit if the trial is successful.
We focus on the problem of uncertainty informed allocation of medical resources (vaccines) to heterogeneous populations for managing epidemic spread. We tackle two related questions: (1) For a compartmental ordinary differential equation (ODE) model of epidemic spread, how can we estimate and integrate parameter uncertainty into resource allocation decisions? (2) How can we computationally handle both nonlinear ODE constraints and parameter uncertainties for a generic stochastic optimization problem for resource allocation? To the best of our knowledge current literature does not fully resolve these questions. Here, we develop a data-driven approach to represent parameter uncertainty accurately and tractably in a novel stochastic optimization problem formulation. We first generate a tractable scenario set by estimating the distribution on ODE model parameters using Bayesian inference with Gaussian processes. Next, we develop a parallelized solution algorithm that accounts for scenario-dependent nonlinear ODE constraints. Our scenario-set generation procedure and solution approach are flexible in that they can handle any compartmental epidemiological ODE model. Our computational experiments on two different non-linear ODE models (SEIR and SEPIHR) indicate that accounting for uncertainty in key epidemiological parameters can improve the efficacy of time-critical allocation decisions by 4-8%. This improvement can be attributed to data-driven and optimal (strategic) nature of vaccine allocations, especially in the early stages of the epidemic when the allocation strategy can crucially impact the long-term trajectory of the disease.
We present Variational Bayesian Network (VBN) - a novel Bayesian entity representation learning model that utilizes hierarchical and relational side information and is particularly useful for modeling entities in the ``long-tail'', where the data is scarce. VBN provides better modeling for long-tail entities via two complementary mechanisms: First, VBN employs informative hierarchical priors that enable information propagation between entities sharing common ancestors. Additionally, VBN models explicit relations between entities that enforce complementary structure and consistency, guiding the learned representations towards a more meaningful arrangement in space. Second, VBN represents entities by densities (rather than vectors), hence modeling uncertainty that plays a complementary role in coping with data scarcity. Finally, we propose a scalable Variational Bayes optimization algorithm that enables fast approximate Bayesian inference. We evaluate the effectiveness of VBN on linguistic, recommendations, and medical inference tasks. Our findings show that VBN outperforms other existing methods across multiple datasets, and especially in the long-tail.
Modern Bayesian inference involves a mixture of computational techniques for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows for data analysis. Typical problems in Bayesian workflows are the approximation of intractable posterior distributions for diverse model types and the comparison of competing models of the same process in terms of their complexity and predictive performance. This manuscript introduces the Python library BayesFlow for simulation-based training of established neural network architectures for amortized data compression and inference. Amortized Bayesian inference, as implemented in BayesFlow, enables users to train custom neural networks on model simulations and re-use these networks for any subsequent application of the models. Since the trained networks can perform inference almost instantaneously, the upfront neural network training is quickly amortized.
Recently, there has been extensive research on the capabilities of biologically plausible algorithms. In this work, we show how one of such algorithms, called predictive coding, is able to perform causal inference tasks. First, we show how a simple change in the inference process of predictive coding enables to compute interventions without the need to mutilate or redefine a causal graph. Then, we explore applications in cases where the graph is unknown, and has to be inferred from observational data. Empirically, we show how such findings can be used to improve the performance of predictive coding in image classification tasks, and conclude that such models are able to perform simple end-to-end causal inference tasks.
Alzheimer's disease (AD) is a prominent, worldwide, age-related neurodegenerative disease that currently has no systemic treatment. Strong evidence suggests that permeable amyloid-beta peptide (Abeta) oligomers, astrogliosis and reactive astrocytosis cause neuronal damage in AD. A large amount of Abeta is secreted by astrocytes, which contributes to the total Abeta deposition in the brain. This suggests that astrocytes may also play a role in AD, leading to increased attention to their dynamics and associated mechanisms. Therefore, in the present study, we developed and evaluated novel stochastic models for Abeta growth using ADNI data to predict the effect of astrocytes on AD progression in a clinical trial. In the AD case, accurate prediction is required for a successful clinical treatment plan. Given that AD studies are observational in nature and involve routine patient visits, stochastic models provide a suitable framework for modelling AD. Using the approximate Bayesian computation (ABC) approach, the AD etiology may be modelled as a multi-state disease process. As a result, we use this approach to examine the weak and strong influence of astrocytes at multiple disease progression stages using ADNI data from the baseline to 2-year visits for AD patients whose ages ranged from 50 to 90 years. Based on ADNI data, we discovered that the strong astrocyte effect (i.e., a higher concentration of astrocytes as compared to Abeta) could help to lower or clear the growth of Abeta, which is a key to slowing down AD progression.
How does language inform our downstream thinking? In particular, how do humans make meaning from language--and how can we leverage a theory of linguistic meaning to build machines that think in more human-like ways? In this paper, we propose rational meaning construction, a computational framework for language-informed thinking that combines neural language models with probabilistic models for rational inference. We frame linguistic meaning as a context-sensitive mapping from natural language into a probabilistic language of thought (PLoT)--a general-purpose symbolic substrate for generative world modeling. Our architecture integrates two computational tools that have not previously come together: we model thinking with probabilistic programs, an expressive representation for commonsense reasoning; and we model meaning construction with large language models (LLMs), which support broad-coverage translation from natural language utterances to code expressions in a probabilistic programming language. We illustrate our framework through examples covering four core domains from cognitive science: probabilistic reasoning, logical and relational reasoning, visual and physical reasoning, and social reasoning. In each, we show that LLMs can generate context-sensitive translations that capture pragmatically-appropriate linguistic meanings, while Bayesian inference with the generated programs supports coherent and robust commonsense reasoning. We extend our framework to integrate cognitively-motivated symbolic modules (physics simulators, graphics engines, and planning algorithms) to provide a unified commonsense thinking interface from language. Finally, we explore how language can drive the construction of world models themselves. We hope this work will provide a roadmap towards cognitive models and AI systems that synthesize the insights of both modern and classical computational perspectives.
We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at \url{https://github.com/minyoungkim21/niwmeta}.
Regular blood pressure (BP) monitoring in clinical and ambulatory settings plays a crucial role in the prevention, diagnosis, treatment, and management of cardiovascular diseases. Recently, the widespread adoption of ambulatory BP measurement devices has been driven predominantly by the increased prevalence of hypertension and its associated risks and clinical conditions. Recent guidelines advocate for regular BP monitoring as part of regular clinical visits or even at home. This increased utilization of BP measurement technologies has brought up significant concerns, regarding the accuracy of reported BP values across settings. In this survey, focusing mainly on cuff-based BP monitoring technologies, we highlight how BP measurements can demonstrate substantial biases and variances due to factors such as measurement and device errors, demographics, and body habitus. With these inherent biases, the development of a new generation of cuff-based BP devices which use artificial-intelligence (AI) has significant potential. We present future avenues where AI-assisted technologies can leverage the extensive clinical literature on BP-related studies together with the large collections of BP records available in electronic health records. These resources can be combined with machine learning approaches, including deep learning and Bayesian inference, to remove BP measurement biases and to provide individualized BP-related cardiovascular risk indexes.
Symbolic Regression (SR) allows for the discovery of scientific equations from data. To limit the large search space of possible equations, prior knowledge has been expressed in terms of formal grammars that characterize subsets of arbitrary strings. However, there is a mismatch between context-free grammars required to express the set of syntactically correct equations, missing closure properties of the former, and a tree structure of the latter. Our contributions are to (i) compactly express experts' prior beliefs about which equations are more likely to be expected by probabilistic Regular Tree Expressions (pRTE), and (ii) adapt Bayesian inference to make such priors efficiently available for symbolic regression encoded as finite state machines. Our scientific case studies show its effectiveness in soil science to find sorption isotherms and for modeling hyper-elastic materials.
This work deals with the heterogeneous semantic-native communication (SNC) problem. When agents do not share the same communication context, the effectiveness of contextual reasoning (CR) is compromised calling for agents to infer other agents' context. This article proposes a novel framework for solving the inverse problem of CR in SNC using two Bayesian inference methods, namely: Bayesian inverse CR (iCR) and Bayesian inverse linearized CR (iLCR). The first proposed Bayesian iCR method utilizes Markov Chain Monte Carlo (MCMC) sampling to infer the agent's context while being computationally expensive. To address this issue, a Bayesian iLCR method is leveraged which obtains a linearized CR (LCR) model by training a linear neural network. Experimental results show that the Bayesian iLCR method requires less computation and achieves higher inference accuracy compared to Bayesian iCR. Additionally, heterogeneous SNC based on the context obtained through the Bayesian iLCR method shows better communication effectiveness than that of Bayesian iCR. Overall, this work provides valuable insights and methods to improve the effectiveness of SNC in situations where agents have different contexts.
We introduce a library called Push that takes a probabilistic programming approach to Bayesian deep learning (BDL). This library enables concurrent execution of BDL inference algorithms on multi-GPU hardware for neural network (NN) models. To accomplish this, Push introduces an abstraction that represents an input NN as a particle. Push enables easy creation of particles so that an input NN can be replicated and particles can communicate asynchronously so that a variety of parameter updates can be expressed, including common BDL algorithms. Our hope is that Push lowers the barrier to experimenting with BDL by streamlining the scaling of particles across GPUs. We evaluate the scaling behavior of particles on single-node multi-GPU devices on vision and scientific machine learning (SciML) tasks.
Conversational recommender systems (CRS) enhance the expressivity and personalization of recommendations through multiple turns of user-system interaction. Critiquing is a well-known paradigm for CRS that allows users to iteratively refine recommendations by providing feedback about attributes of recommended items. While existing critiquing methodologies utilize direct attributes of items to address user requests such as 'I prefer Western movies', the opportunity of incorporating richer contextual and side information about items stored in Knowledge Graphs (KG) into the critiquing paradigm has been overlooked. Employing this substantial knowledge together with a well-established reasoning methodology paves the way for critique-based recommenders to allow for complex knowledge-based feedback (e.g., 'I like movies featuring war side effects on veterans') which may arise in natural user-system conversations. In this work, we aim to increase the flexibility of critique-based recommendation by integrating KGs and propose a novel Bayesian inference framework that enables reasoning with relational knowledge-based feedback. We study and formulate the framework considering a Gaussian likelihood and evaluate it on two well-known recommendation datasets with KGs. Our evaluations demonstrate the effectiveness of our framework in leveraging indirect KG-based feedback (i.e., preferred relational properties of items rather than preferred items themselves), often improving personalized recommendations over a one-shot recommender by more than 15%. This work enables a new paradigm for using rich knowledge content and reasoning over indirect evidence as a mechanism for critiquing interactions with CRS.
Efficiently sampling from un-normalized target distributions is a fundamental problem in scientific computing and machine learning. Traditional approaches like Markov Chain Monte Carlo (MCMC) guarantee asymptotically unbiased samples from such distributions but suffer from computational inefficiency, particularly when dealing with high-dimensional targets, as they require numerous iterations to generate a batch of samples. In this paper, we propose an efficient and scalable neural implicit sampler that overcomes these limitations. Our sampler can generate large batches of samples with low computational costs by leveraging a neural transformation that directly maps easily sampled latent vectors to target samples without the need for iterative procedures. To train the neural implicit sampler, we introduce two novel methods: the KL training method and the Fisher training method. The former minimizes the Kullback-Leibler divergence, while the latter minimizes the Fisher divergence. By employing these training methods, we effectively optimize the neural implicit sampler to capture the desired target distribution. To demonstrate the effectiveness, efficiency, and scalability of our proposed samplers, we evaluate them on three sampling benchmarks with different scales. These benchmarks include sampling from 2D targets, Bayesian inference, and sampling from high-dimensional energy-based models (EBMs). Notably, in the experiment involving high-dimensional EBMs, our sampler produces samples that are comparable to those generated by MCMC-based methods while being more than 100 times more efficient, showcasing the efficiency of our neural sampler. We believe that the theoretical and empirical contributions presented in this work will stimulate further research on developing efficient samplers for various applications beyond the ones explored in this study.
In-context learning (ICL) is one of the surprising and useful features of large language models and subject of intense research. Recently, stylized meta-learning-like ICL setups have been devised that train transformers on sequences of input-output pairs $(x, f(x))$. The function $f$ comes from a function class and generalization is checked by evaluating on sequences generated from unseen functions from the same class. One of the main discoveries in this line of research has been that for several function classes, such as linear regression, transformers successfully generalize to new functions in the class. However, the inductive biases of these models resulting in this behavior are not clearly understood. A model with unlimited training data and compute is a Bayesian predictor: it learns the pretraining distribution. In this paper we empirically examine how far this Bayesian perspective can help us understand ICL. To this end, we generalize the previous meta-ICL setup to hierarchical meta-ICL setup which involve unions of multiple task families. We instantiate this setup on a diverse range of linear and nonlinear function families and find that transformers can do ICL in this setting as well. Where Bayesian inference is tractable, we find evidence that high-capacity transformers mimic the Bayesian predictor. The Bayesian perspective provides insights into the inductive bias of ICL and how transformers perform a particular task when they are trained on multiple tasks. We also find that transformers can learn to generalize to new function classes that were not seen during pretraining. This involves deviation from the Bayesian predictor. We examine these deviations in more depth offering new insights and hypotheses.
The transition to Electric Vehicles (EV) in place of traditional internal combustion engines is increasing societal demand for electricity. The ability to integrate the additional demand from EV charging into forecasting electricity demand is critical for maintaining the reliability of electricity generation and distribution. Load forecasting studies typically exclude households with home EV charging, focusing on offices, schools, and public charging stations. Moreover, they provide point forecasts which do not offer information about prediction uncertainty. Consequently, this paper proposes the Long Short-Term Memory Bayesian Neural Networks (LSTM-BNNs) for household load forecasting in presence of EV charging. The approach takes advantage of the LSTM model to capture the time dependencies and uses the dropout layer with Bayesian inference to generate prediction intervals. Results show that the proposed LSTM-BNNs achieve accuracy similar to point forecasts with the advantage of prediction intervals. Moreover, the impact of lockdowns related to the COVID-19 pandemic on the load forecasting model is examined, and the analysis shows that there is no major change in the model performance as, for the considered households, the randomness of the EV charging outweighs the change due to pandemic.
We propose the stochastic optimal path which solves the classical optimal path problem by a probability-softening solution. This unified approach transforms a wide range of DP problems into directed acyclic graphs in which all paths follow a Gibbs distribution. We show the equivalence of the Gibbs distribution to a message-passing algorithm by the properties of the Gumbel distribution and give all the ingredients required for variational Bayesian inference of a latent path, namely Bayesian dynamic programming (BDP). We demonstrate the usage of BDP in the latent space of variational autoencoders (VAEs) and propose the BDP-VAE which captures structured sparse optimal paths as latent variables. This enables end-to-end training for generative tasks in which models rely on unobserved structural information. At last, we validate the behavior of our approach and showcase its applicability in two real-world applications: text-to-speech and singing voice synthesis. Our implementation code is available at \url{https://github.com/XinleiNIU/LatentOptimalPathsBayesianDP}.