This paper studies the theoretical framework of the alignment process of generative models with Reinforcement Learning from Human Feedback (RLHF). We consider a standard mathematical formulation, the reverse-KL regularized contextual bandit for RLHF. Despite its widespread practical application, a rigorous theoretical analysis of this formulation remains open. We investigate its theoretical properties both in offline and online settings and propose efficient algorithms with finite-sample theoretical guarantees. Our work bridges the gap between theory and practice by linking our theoretical insights with existing practical alignment algorithms such as Direct Preference Optimization (DPO) and Rejection Sampling Optimization (RSO). Furthermore, these findings and connections also offer both theoretical and practical communities new tools and insights for future algorithmic design of alignment algorithms.

Vesicoureteral Reflux (VUR) is a pediatric disorder in which urine flows backwards from the bladder to the upper urinary tract. Its detection is of great importance as it increases the risk of a Urinary Tract Infection, which can then lead to a kidney infection since bacteria may have direct access to the kidneys. Unfortunately the detection of VUR requires a rather painful medical examination, called voiding cysteourethrogram (VCUG), that exposes the child to radiation. In an effort to avoid the exposure to radiation required by VCUG some recent studies examined the use of machine learning techniques for the detection of VUR based on data that can be obtained without exposing the child to radiation. This work takes one step further by proposing an approach that provides lower and upper bounds for the conditional probability of a given child having VUR. The important property of these bounds is that they are guaranteed (up to statistical fluctuations) to contain well-calibrated probabilities with the only requirement that observations are independent and identically distributed (i.i.d.). Therefore they are much more informative and reliable than the plain yes/no answers provided by other techniques.

In practice, it is essential to compare and rank candidate policies offline before real-world deployment for safety and reliability. Prior work seeks to solve this offline policy ranking (OPR) problem through value-based methods, such as Off-policy evaluation (OPE). However, they fail to analyze special cases performance (e.g., worst or best cases), due to the lack of holistic characterization of policies performance. It is even more difficult to estimate precise policy values when the reward is not fully accessible under sparse settings. In this paper, we present Probabilistic Offline Policy Ranking (POPR), a framework to address OPR problems by leveraging expert data to characterize the probability of a candidate policy behaving like experts, and approximating its entire performance posterior distribution to help with ranking. POPR does not rely on value estimation, and the derived performance posterior can be used to distinguish candidates in worst, best, and average-cases. To estimate the posterior, we propose POPR-EABC, an Energy-based Approximate Bayesian Computation (ABC) method conducting likelihood-free inference. POPR-EABC reduces the heuristic nature of ABC by a smooth energy function, and improves the sampling efficiency by a pseudo-likelihood. We empirically demonstrate that POPR-EABC is adequate for evaluating policies in both discrete and continuous action spaces across various experiment environments, and facilitates probabilistic comparisons of candidate policies before deployment.

Re-training a deep learning model each time a single data point receives a new label is impractical due to the inherent complexity of the training process. Consequently, existing active learning (AL) algorithms tend to adopt a batch-based approach where, during each AL iteration, a set of data points is collectively chosen for annotation. However, this strategy frequently leads to redundant sampling, ultimately eroding the efficacy of the labeling procedure. In this paper, we introduce a new AL algorithm that harnesses the power of a Gaussian process surrogate in conjunction with the neural network principal learner. Our proposed model adeptly updates the surrogate learner for every new data instance, enabling it to emulate and capitalize on the continuous learning dynamics of the neural network without necessitating a complete retraining of the principal model for each individual label. Experiments on four benchmark datasets demonstrate that this approach yields significant enhancements, either rivaling or aligning with the performance of state-of-the-art techniques.

Classification and probability estimation have broad applications in modern machine learning and data science applications, including biology, medicine, engineering, and computer science. The recent development of a class of weighted Support Vector Machines (wSVMs) has shown great values in robustly predicting the class probability and classification for various problems with high accuracy. The current framework is based on the $\ell^2$-norm regularized binary wSVMs optimization problem, which only works with dense features and has poor performance at sparse features with redundant noise in most real applications. The sparse learning process requires a prescreen of the important variables for each binary wSVMs for accurately estimating pairwise conditional probability. In this paper, we proposed novel wSVMs frameworks that incorporate automatic variable selection with accurate probability estimation for sparse learning problems. We developed efficient algorithms for effective variable selection for solving either the $\ell^1$-norm or elastic net regularized binary wSVMs optimization problems. The binary class probability is then estimated either by the $\ell^2$-norm regularized wSVMs framework with selected variables or by elastic net regularized wSVMs directly. The two-step approach of $\ell^1$-norm followed by $\ell^2$-norm wSVMs show a great advantage in both automatic variable selection and reliable probability estimators with the most efficient time. The elastic net regularized wSVMs offer the best performance in terms of variable selection and probability estimation with the additional advantage of variable grouping in the compensation of more computation time for high dimensional problems. The proposed wSVMs-based sparse learning methods have wide applications and can be further extended to $K$-class problems through ensemble learning.

Traditional neural networks are simple to train but they typically produce overconfident predictions. In contrast, Bayesian neural networks provide good uncertainty quantification but optimizing them is time consuming due to the large parameter space. This paper proposes to combine the advantages of both approaches by performing Variational Inference in the Final layer Output space (VIFO), because the output space is much smaller than the parameter space. We use neural networks to learn the mean and the variance of the probabilistic output. Like standard, non-Beyesian models, VIFO enjoys simple training and one can use Rademacher complexity to provide risk bounds for the model. On the other hand, using the Bayesian formulation we incorporate collapsed variational inference with VIFO which significantly improves the performance in practice. Experiments show that VIFO and ensembles of VIFO provide a good tradeoff in terms of run time and uncertainty quantification, especially for out of distribution data.

This article considers Bayesian model selection via mean-field (MF) variational approximation. Towards this goal, we study the non-asymptotic properties of MF inference under the Bayesian framework that allows latent variables and model mis-specification. Concretely, we show a Bernstein von-Mises (BvM) theorem for the variational distribution from MF under possible model mis-specification, which implies the distributional convergence of MF variational approximation to a normal distribution centering at the maximal likelihood estimator (within the specified model). Motivated by the BvM theorem, we propose a model selection criterion using the evidence lower bound (ELBO), and demonstrate that the model selected by ELBO tends to asymptotically agree with the one selected by the commonly used Bayesian information criterion (BIC) as sample size tends to infinity. Comparing to BIC, ELBO tends to incur smaller approximation error to the log-marginal likelihood (a.k.a. model evidence) due to a better dimension dependence and full incorporation of the prior information. Moreover, we show the geometric convergence of the coordinate ascent variational inference (CAVI) algorithm under the parametric model framework, which provides a practical guidance on how many iterations one typically needs to run when approximating the ELBO. These findings demonstrate that variational inference is capable of providing a computationally efficient alternative to conventional approaches in tasks beyond obtaining point estimates, which is also empirically demonstrated by our extensive numerical experiments.

Deep Learning models have achieved remarkable performance in tasks such as image classification or generation, often surpassing human accuracy. However, they can struggle to learn new tasks and update their knowledge without access to previous data, leading to a significant loss of accuracy known as Catastrophic Forgetting (CF). This phenomenon was first observed by McCloskey and Cohen in 1989 and remains an active research topic. Incremental learning without forgetting is widely recognized as a crucial aspect in building better AI systems, as it allows models to adapt to new tasks without losing the ability to perform previously learned ones. This article surveys recent studies that tackle CF in modern Deep Learning models that use gradient descent as their learning algorithm. Although several solutions have been proposed, a definitive solution or consensus on assessing CF is yet to be established. The article provides a comprehensive review of recent solutions, proposes a taxonomy to organize them, and identifies research gaps in this area.

In this paper, we critically evaluate Bayesian methods for uncertainty estimation in deep learning, focusing on the widely applied Laplace approximation and its variants. Our findings reveal that the conventional method of fitting the Hessian matrix negatively impacts out-of-distribution (OOD) detection efficiency. We propose a different point of view, asserting that focusing solely on optimizing prior precision can yield more accurate uncertainty estimates in OOD detection while preserving adequate calibration metrics. Moreover, we demonstrate that this property is not connected to the training stage of a model but rather to its intrinsic properties. Through extensive experimental evaluation, we establish the superiority of our simplified approach over traditional methods in the out-of-distribution domain.

Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in treatment effect estimation to support decision-making in a relatively small sample size setting. Our proposed model places Gaussian process priors on the nonparametric components of a semiparametric model called a partially linear model. This model formulation has three advantages. First, we can analytically compute the posterior distribution of a treatment effect without relying on the computationally demanding posterior approximation. Second, we can guarantee that the posterior distribution concentrates around the true one as the sample size goes to infinity. Third, we can incorporate prior knowledge about a treatment effect into the prior distribution, improving the estimation efficiency. Our experimental results show that even in the small sample size setting, our method can accurately estimate the heterogeneous treatment effects and effectively quantify its estimation uncertainty.