The practical utility of agent-based models in decision-making relies on their capacity to accurately replicate populations while seamlessly integrating real-world data streams. Yet, the incorporation of such data poses significant challenges due to privacy concerns. To address this issue, we introduce a paradigm for private agent-based modeling wherein the simulation, calibration, and analysis of agent-based models can be achieved without centralizing the agents attributes or interactions. The key insight is to leverage techniques from secure multi-party computation to design protocols for decentralized computation in agent-based models. This ensures the confidentiality of the simulated agents without compromising on simulation accuracy. We showcase our protocols on a case study with an epidemiological simulation comprising over 150,000 agents. We believe this is a critical step towards deploying agent-based models to real-world applications.

Depression is a significant issue nowadays. As per the World Health Organization (WHO), in 2023, over 280 million individuals are grappling with depression. This is a huge number; if not taken seriously, these numbers will increase rapidly. About 4.89 billion individuals are social media users. People express their feelings and emotions on platforms like Twitter, Facebook, Reddit, Instagram, etc. These platforms contain valuable information which can be used for research purposes. Considerable research has been conducted across various social media platforms. However, certain limitations persist in these endeavors. Particularly, previous studies were only focused on detecting depression and the intensity of depression in tweets. Also, there existed inaccuracies in dataset labeling. In this research work, five types of depression (Bipolar, major, psychotic, atypical, and postpartum) were predicted using tweets from the Twitter database based on lexicon labeling. Explainable AI was used to provide reasoning by highlighting the parts of tweets that represent type of depression. Bidirectional Encoder Representations from Transformers (BERT) was used for feature extraction and training. Machine learning and deep learning methodologies were used to train the model. The BERT model presented the most promising results, achieving an overall accuracy of 0.96.

Bayesian optimization (BO) algorithm is very popular for solving low-dimensional expensive optimization problems. Extending Bayesian optimization to high dimension is a meaningful but challenging task. One of the major challenges is that it is difficult to find good infill solutions as the acquisition functions are also high-dimensional. In this work, we propose the expected coordinate improvement (ECI) criterion for high-dimensional Bayesian optimization. The proposed ECI criterion measures the potential improvement we can get by moving the current best solution along one coordinate. The proposed approach selects the coordinate with the highest ECI value to refine in each iteration and covers all the coordinates gradually by iterating over the coordinates. The greatest advantage of the proposed ECI-BO (expected coordinate improvement based Bayesian optimization) algorithm over the standard BO algorithm is that the infill selection problem of the proposed algorithm is always a one-dimensional problem thus can be easily solved. Numerical experiments show that the proposed algorithm can achieve significantly better results than the standard BO algorithm and competitive results when compared with five state-of-the-art high-dimensional BOs. This work provides a simple but efficient approach for high-dimensional Bayesian optimization.

Language models (LMs) trained on vast quantities of text data can acquire sophisticated skills such as generating summaries, answering questions or generating code. However, they also manifest behaviors that violate human preferences, e.g., they can generate offensive content, falsehoods or perpetuate social biases. In this thesis, I explore several approaches to aligning LMs with human preferences. First, I argue that aligning LMs can be seen as Bayesian inference: conditioning a prior (base, pretrained LM) on evidence about human preferences (Chapter 2). Conditioning on human preferences can be implemented in numerous ways. In Chapter 3, I investigate the relation between two approaches to finetuning pretrained LMs using feedback given by a scoring function: reinforcement learning from human feedback (RLHF) and distribution matching. I show that RLHF can be seen as a special case of distribution matching but distributional matching is strictly more general. In chapter 4, I show how to extend the distribution matching to conditional language models. Finally, in chapter 5 I explore a different root: conditioning an LM on human preferences already during pretraining. I show that involving human feedback from the very start tends to be more effective than using it only during supervised finetuning. Overall, these results highlight the room for alignment techniques different from and complementary to RLHF.

We study the problem of learning directed acyclic graphs from continuous observational data, generated according to a linear Gaussian structural equation model. State-of-the-art structure learning methods for this setting have at least one of the following shortcomings: i) they cannot provide optimality guarantees and can suffer from learning sub-optimal models; ii) they rely on the stringent assumption that the noise is homoscedastic, and hence the underlying model is fully identifiable. We overcome these shortcomings and develop a computationally efficient mixed-integer programming framework for learning medium-sized problems that accounts for arbitrary heteroscedastic noise. We present an early stopping criterion under which we can terminate the branch-and-bound procedure to achieve an asymptotically optimal solution and establish the consistency of this approximate solution. In addition, we show via numerical experiments that our method outperforms three state-of-the-art algorithms and is robust to noise heteroscedasticity, whereas the performance of the competing methods deteriorates under strong violations of the identifiability assumption. The software implementation of our method is available as the Python package \emph{micodag}.

We consider the problem of estimating probability density functions based on sample data, using a finite mixture of densities from some component class. To this end, we introduce the $h$-lifted Kullback--Leibler (KL) divergence as a generalization of the standard KL divergence and a criterion for conducting risk minimization. Under a compact support assumption, we prove an $\mc{O}(1/{\sqrt{n}})$ bound on the expected estimation error when using the $h$-lifted KL divergence, which extends the results of Rakhlin et al. (2005, ESAIM: Probability and Statistics, Vol. 9) and Li and Barron (1999, Advances in Neural Information ProcessingSystems, Vol. 12) to permit the risk bounding of density functions that are not strictly positive. We develop a procedure for the computation of the corresponding maximum $h$-lifted likelihood estimators ($h$-MLLEs) using the Majorization-Maximization framework and provide experimental results in support of our theoretical bounds.

Large language models primarily rely on inductive reasoning for decision making. This results in unreliable decisions when applied to real-world tasks that often present incomplete contexts and conditions. Thus, accurate probability estimation and appropriate interpretations are required to enhance decision-making reliability. In this paper, we propose a Bayesian inference framework called BIRD for large language models. BIRD provides controllable and interpretable probability estimation for model decisions, based on abductive factors, LLM entailment, as well as learnable deductive Bayesian modeling. Experiments show that BIRD produces probability estimations that align with human judgments over 65% of the time using open-sourced Llama models, outperforming the state-of-the-art GPT-4 by 35%. We also show that BIRD can be directly used for trustworthy decision making on many real-world applications.

The purpose of this paper is twofold. First, we propose a novel algorithm for estimating parameters in one-dimensional Gaussian mixture models (GMMs). The algorithm takes advantage of the Hankel structure inherent in the Fourier data obtained from independent and identically distributed (i.i.d) samples of the mixture. For GMMs with a unified variance, a singular value ratio functional using the Fourier data is introduced and used to resolve the variance and component number simultaneously. The consistency of the estimator is derived. Compared to classic algorithms such as the method of moments and the maximum likelihood method, the proposed algorithm does not require prior knowledge of the number of Gaussian components or good initial guesses. Numerical experiments demonstrate its superior performance in estimation accuracy and computational cost. Second, we reveal that there exists a fundamental limit to the problem of estimating the number of Gaussian components or model order in the mixture model if the number of i.i.d samples is finite. For the case of a single variance, we show that the model order can be successfully estimated only if the minimum separation distance between the component means exceeds a certain threshold value and can fail if below. We derive a lower bound for this threshold value, referred to as the computational resolution limit, in terms of the number of i.i.d samples, the variance, and the number of Gaussian components. Numerical experiments confirm this phase transition phenomenon in estimating the model order. Moreover, we demonstrate that our algorithm achieves better scores in likelihood, AIC, and BIC when compared to the EM algorithm.

We propose a novel method (floZ), based on normalizing flows, for estimating the Bayesian evidence (and its numerical uncertainty) from a set of samples drawn from the unnormalized posterior distribution. We validate it on distributions whose evidence is known analytically, up to 15 parameter space dimensions, and compare with two state-of-the-art techniques for estimating the evidence: nested sampling (which computes the evidence as its main target) and a k-nearest-neighbors technique that produces evidence estimates from posterior samples. Provided representative samples from the target posterior are available, our method is more robust to posterior distributions with sharp features, especially in higher dimensions. It has wide applicability, e.g., to estimate the evidence from variational inference, Markov-chain Monte Carlo samples, or any other method that delivers samples from the unnormalized posterior density.

Parallelisation in Bayesian optimisation is a common strategy but faces several challenges: the need for flexibility in acquisition functions and kernel choices, flexibility dealing with discrete and continuous variables simultaneously, model misspecification, and lastly fast massive parallelisation. To address these challenges, we introduce a versatile and modular framework for batch Bayesian optimisation via probabilistic lifting with kernel quadrature, called SOBER, which we present as a Python library based on GPyTorch/BoTorch. Our framework offers the following unique benefits: (1) Versatility in downstream tasks under a unified approach.