State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dynamical systems. In comparison to conventional parametric models, we offer the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting. Our main algorithm uses a hybrid inference approach combining variational Bayes and sequential Monte Carlo.

Video summarization is a challenging problem with great application potential. Whereas prior approaches, largely unsupervised in nature, focus on sampling useful frames and assembling them as summaries, we consider video summarization as a supervised subset selection problem. Our idea is to teach the system to learn from human-created summaries how to select informative and diverse subsets, so as to best meet evaluation metrics derived from human-perceived quality. To this end, we propose the sequential determinantal point process (seqDPP), a probabilistic model for diverse sequential subset selection. Our novel seqDPP heeds the inherent sequential structures in video data, thus overcoming the deficiency of the standard DPP, which treats video frames as randomly permutable items. Meanwhile, seqDPP retains the power of modeling diverse subsets, essential for summarization. Our extensive results of summarizing videos from 3 datasets demonstrate the superior performance of our method, compared to not only existing unsupervised methods but also naive applications of the standard DPP model.

Any reinforcement learning algorithm that applies to all Markov decision processes (MDPs) will su er (Ô SAT) regret on some MDP, where T is the elapsed time and S and A are the cardinalities of the state and action spaces. This implies T = (SA) time to guarantee a near-optimal policy. In many settings of practical interest, due to the curse of dimensionality, S and A can be so enormous that this learning time is unacceptable. We establish that, if the system is known to be a factored MDP, it is possible to achieve regret that scales polynomially in the number of parameters encoding the factored MDP, which may be exponentially smaller than S or A. We provide two algorithms that satisfy near-optimal regret bounds in this context: posterior sampling reinforcement learning (PSRL) and an upper confidence bound algorithm (UCRL-Factored).

We study the sensitivity of a MAP configuration of a discrete probabilistic graphical model with respect to perturbations of its parameters. These perturbations are global, in the sense that simultaneous perturbations of all the parameters (or any chosen subset of them) are allowed. Our main contribution is an exact algorithm that can check whether the MAP configuration is robust with respect to given perturbations. Its complexity is essentially the same as that of obtaining the MAP configuration itself, so it can be promptly used with minimal effort. We use our algorithm to identify the largest global perturbation that does not induce a change in the MAP configuration, and we successfully apply this robustness measure in two practical scenarios: the prediction of facial action units with posed images and the classification of multiple real public data sets. A strong correlation between the proposed robustness measure and accuracy is verified in both scenarios.

This paper is concerned with compressive sensing of signals drawn from a Gaussian mixture model (GMM) with sparse precision matrices. Previous work has shown: (i) a signal drawn from a given GMM can be perfectly reconstructed from r noise-free measurements if the (dominant) rank of each covariance matrix is less than r; (ii) a sparse Gaussian graphical model can be efficiently estimated from fully-observed training signals using graphical lasso. This paper addresses a problem more challenging than both (i) and (ii), by assuming that the GMM is unknown and each signal is only observed through incomplete linear measurements. Under these challenging assumptions, we develop a hierarchical Bayesian method to simultaneously estimate the GMM and recover the signals using solely the incomplete measurements and a Bayesian shrinkage prior that promotes sparsity of the Gaussian precision matrices. In addition, we provide theoretical performance bounds to relate the reconstruction error to the number of signals for which measurements are available, the sparsity level of precision matrices, and the "incompleteness" of measurements. The proposed method is demonstrated extensively on compressive sensing of imagery and video, and the results with simulated and hardware-acquired real measurements show significant performance improvement over state-of-the-art methods.

Multilayer Neural Networks (MNNs) are commonly trained using gradient descent-based methods, such as BackPropagation (BP). Inference in probabilistic graphical models is often done using variational Bayes methods, such as Expectation Propagation (EP). We show how an EP based approach can also be used to train deterministic MNNs. Specifically, we approximate the posterior of the weights given the data using a "mean-field" factorized distribution, in an online setting. Using online EP and the central limit theorem we find an analytical approximation to the Bayes update of this posterior, as well as the resulting Bayes estimates of the weights and outputs. Despite a different origin, the resulting algorithm, Expectation BackPropagation (EBP), is very similar to BP in form and efficiency. However, it has several additional advantages: (1) Training is parameter-free, given initial conditions (prior) and the MNN architecture. This is useful for large-scale problems, where parameter tuning is a major challenge.

Weaknesses: - Central parts of the paper are unclear eg. in line 80 \log P_M (X; \theta) should be the negative cross entropy. The only quantitative results are on adaptation from USPS to MNIST in line 268. However, prior work [1] achieves 96.5% accuracy in comparison to the 55% accuracy achieved by the proposed method. It would be desirable to evaluate the proposed approach on the more complex Facades/Maps/Cityscapes using the MSE metric to facilitate comparison with AlignFlow and [1]. It is unclear how the inductive bias from each of the datasets influence the shared space.

After discussion, all reviewers, and the meta-reviewer, agree that the paper should be accepted. As the authors show, the method in its current form may not scale well to higher dimensions. While a method without this limitation would obviously be preferable, the reviewers agree that this limitation can be addressed in future work, where the connection with GANs that the authors establish may be helpful.

Recent AI agents, such as ChatGPT and LLaMA, primarily rely on instruction tuning and reinforcement learning to calibrate the output of large language models (LLMs) with human intentions, ensuring the outputs are harmless and helpful. Existing methods heavily depend on the manual annotation of high-quality positive samples, while contending with issues such as noisy labels and minimal distinctions between preferred and dispreferred response data. However, readily available toxic samples with clear safety distinctions are often filtered out, removing valuable negative references that could aid LLMs in safety alignment. In response, we propose PT-ALIGN, a novel safety self-alignment approach that minimizes human supervision by automatically refining positive and toxic samples and performing fine-grained dual instruction tuning. Positive samples are harmless responses, while toxic samples deliberately contain extremely harmful content, serving as a new supervisory signals. Specifically, we utilize LLM itself to iteratively generate and refine training instances by only exploring fewer than 50 human annotations. We then employ two losses, i.e., maximum likelihood estimation (MLE) and fine-grained unlikelihood training (UT), to jointly learn to enhance the LLM's safety. The MLE loss encourages an LLM to maximize the generation of harmless content based on positive samples. Conversely, the fine-grained UT loss guides the LLM to minimize the output of harmful words based on negative samples at the token-level, thereby guiding the model to decouple safety from effectiveness, directing it toward safer fine-tuning objectives, and increasing the likelihood of generating helpful and reliable content. Experiments on 9 popular open-source LLMs demonstrate the effectiveness of our PT-ALIGN for safety alignment, while maintaining comparable levels of helpfulness and usefulness.

Offline preference alignment for language models such as Direct Preference Optimization (DPO) is favored for its effectiveness and simplicity, eliminating the need for costly reinforcement learning. Various offline algorithms have been developed for different data settings, yet they lack a unified understanding. In this study, we introduce Pior-Informed Preference Alignment (PIPA), a unified, RL-free probabilistic framework that formulates language model preference alignment as a Maximum Likelihood Estimation (MLE) problem with prior constraints. This method effectively accommodates both paired and unpaired data, as well as answer and step-level annotations. We illustrate that DPO and KTO are special cases with different prior constraints within our framework. By integrating different types of prior information, we developed two variations of PIPA: PIPA-M and PIPA-N. Both algorithms demonstrate a $3\sim10\%$ performance enhancement on the GSM8K and MATH benchmarks across all configurations, achieving these gains without additional training or computational costs compared to existing algorithms.