Discrete diffusion models with absorbing processes have shown promise in language modeling. The key quantities to be estimated are the ratios between the marginal probabilities of two transitive states at all timesteps, called the concrete score. In this paper, we reveal that the concrete score in absorbing diffusion can be expressed as conditional probabilities of clean data, multiplied by a time-dependent scalar in an analytic form. Motivated by this finding, we propose reparameterized absorbing discrete diffusion (RADD), a dedicated diffusion model without time-condition that characterizes the time-independent conditional probabilities. Besides its simplicity, RADD can reduce the number of function evaluations (NFEs) by caching the output of the time-independent network when the noisy sample remains unchanged in a sampling interval. Empirically, RADD is up to 3.5 times faster while achieving similar performance with the strongest baseline. Built upon the new perspective of conditional distributions, we further unify absorbing discrete diffusion and any-order autoregressive models (AO-ARMs), showing that the upper bound on the negative log-likelihood for the diffusion model can be interpreted as an expected negative log-likelihood for AO-ARMs. Further, our RADD models achieve SOTA performance among diffusion models on 5 zero-shot language modeling benchmarks (measured by perplexity) at the GPT-2 scale. Our code is available at https://github.com/ML-GSAI/RADD.

Post-nonlinear (PNL) causal models stand out as a versatile and adaptable framework for modeling intricate causal relationships. However, accurately capturing the invertibility constraint required in PNL models remains challenging in existing studies. To address this problem, we introduce CAF-PoNo (Causal discovery via Normalizing Flows for Post-Nonlinear models), harnessing the power of the normalizing flows architecture to enforce the crucial invertibility constraint in PNL models. Through normalizing flows, our method precisely reconstructs the hidden noise, which plays a vital role in cause-effect identification through statistical independence testing. Furthermore, the proposed approach exhibits remarkable extensibility, as it can be seamlessly expanded to facilitate multivariate causal discovery via causal order identification, empowering us to efficiently unravel complex causal relationships. Extensive experimental evaluations on both simulated and real datasets consistently demonstrate that the proposed method outperforms several state-of-the-art approaches in both bivariate and multivariate causal discovery tasks.

Bayesian causal discovery offers the power to quantify epistemic uncertainties among a broad range of structurally diverse causal theories potentially explaining the data, represented in forms of directed acyclic graphs (DAGs). However, existing methods struggle with efficient DAG sampling due to the complex acyclicity constraint. In this study, we propose a scalable Bayesian approach to effectively learn the posterior distribution over causal graphs given observational data thanks to the ability to generate DAGs without explicitly enforcing acyclicity. Specifically, we introduce a novel differentiable DAG sampling method that can generate a valid acyclic causal graph by mapping an unconstrained distribution of implicit topological orders to a distribution over DAGs. Given this efficient DAG sampling scheme, we are able to model the posterior distribution over causal graphs using a simple variational distribution over a continuous domain, which can be learned via the variational inference framework. Extensive empirical experiments on both simulated and real datasets demonstrate the superior performance of the proposed model compared to several state-of-the-art baselines.

This study proposes the use of a social learning method to estimate a global state within a multi-agent off-policy actor-critic algorithm for reinforcement learning (RL) operating in a partially observable environment. We assume that the network of agents operates in a fully-decentralized manner, possessing the capability to exchange variables with their immediate neighbors. The proposed design methodology is supported by an analysis demonstrating that the difference between final outcomes, obtained when the global state is fully observed versus estimated through the social learning method, is $\varepsilon$-bounded when an appropriate number of iterations of social learning updates are implemented. Unlike many existing dec-POMDP-based RL approaches, the proposed algorithm is suitable for model-free multi-agent reinforcement learning as it does not require knowledge of a transition model. Furthermore, experimental results illustrate the efficacy of the algorithm and demonstrate its superiority over the current state-of-the-art methods.

In supervised classification, we use a training set of labeled observations from different competing classes to form a decision rule for classifying unlabeled test set observations as accurately as possible. Starting from Fisher (1936), Rao (1948) and Fix and Hodges (1951), several parametric as well as nonparametric classifiers have been developed for this purpose (see, e.g., Duda et al., 2007; Hastie et al., 2009). Among them, the nearest neighbor classifier (see, e.g., Cover and Hart, 1967) is perhaps the most popular one. The k-nearest neighbor classifier (k-NN) classifies an observation x to the class having the maximum number of representatives among the k nearest neighbors of x. This classifier works well if the training sample size is large compared to the dimension of the data. For a suitable choice of k (which increases with the training sample size at an appropriate rate), under some mild regularity conditions, the misclassification rate of the k-NN classifier converges to the Bayes risk (i.e., the misclassification rate of the Bayes classifier) as the training sample size grows to infinity (see, e.g.

We develop a novel measurement framework based on a Gaussian process coregionalization model to address a long-lasting debate in psychometrics: whether psychological features like personality share a common structure across the population, vary uniquely for individuals, or some combination. We propose the idiographic personality Gaussian process (IPGP) framework, an intermediate model that accommodates both shared trait structure across a population and "idiographic" deviations for individuals. IPGP leverages the Gaussian process coregionalization model to handle the grouped nature of battery responses, but adjusted to non-Gaussian ordinal data. We further exploit stochastic variational inference for efficient latent factor estimation required for idiographic modeling at scale. Using synthetic and real data, we show that IPGP improves both prediction of actual responses and estimation of individualized factor structures relative to existing benchmarks. In a third study, we show that IPGP also identifies unique clusters of personality taxonomies in real-world data, displaying great potential in advancing individualized approaches to psychological diagnosis and treatment.

We propose a randomized physics-informed neural network (PINN) or rPINN method for uncertainty quantification in inverse partial differential equation (PDE) problems with noisy data. This method is used to quantify uncertainty in the inverse PDE PINN solutions. Recently, the Bayesian PINN (BPINN) method was proposed, where the posterior distribution of the PINN parameters was formulated using the Bayes' theorem and sampled using approximate inference methods such as the Hamiltonian Monte Carlo (HMC) and variational inference (VI) methods. In this work, we demonstrate that HMC fails to converge for non-linear inverse PDE problems. As an alternative to HMC, we sample the distribution by solving the stochastic optimization problem obtained by randomizing the PINN loss function. The effectiveness of the rPINN method is tested for linear and non-linear Poisson equations, and the diffusion equation with a high-dimensional space-dependent diffusion coefficient. The rPINN method provides informative distributions for all considered problems. For the linear Poisson equation, HMC and rPINN produce similar distributions, but rPINN is on average 27 times faster than HMC. For the non-linear Poison and diffusion equations, the HMC method fails to converge because a single HMC chain cannot sample multiple modes of the posterior distribution of the PINN parameters in a reasonable amount of time.

The vehicular metaverse is envisioned as a blended immersive domain that promises to bring revolutionary changes to the automotive industry. As a core component of vehicular metaverses, Vehicle Twins (VTs) are digital twins that cover the entire life cycle of vehicles, providing immersive virtual services for Vehicular Metaverse Users (VMUs). Vehicles with limited resources offload the computationally intensive tasks of constructing and updating VTs to edge servers and migrate VTs between these servers, ensuring seamless and immersive experiences for VMUs. However, the high mobility of vehicles, uneven deployment of edge servers, and potential security threats pose challenges to achieving efficient and reliable VT migrations. To address these issues, we propose a secure and reliable VT migration framework in vehicular metaverses. Specifically, we design a two-layer trust evaluation model to comprehensively evaluate the reputation value of edge servers in the network communication and interaction layers. Then, we model the VT migration problem as a partially observable Markov decision process and design a hybrid-Generative Diffusion Model (GDM) algorithm based on deep reinforcement learning to generate optimal migration decisions by taking hybrid actions (i.e., continuous actions and discrete actions). Numerical results demonstrate that the hybrid-GDM algorithm outperforms the baseline algorithms, showing strong adaptability in various settings and highlighting the potential of the hybrid-GDM algorithm for addressing various optimization issues in vehicular metaverses.

State-of-the-art language models are autoregressive and operate on subword units known as tokens. Specifically, one must encode the conditioning string into a list of tokens before passing to the language models for next-token prediction. We show that popular encoding schemes, such as maximum prefix encoding (MPE) and byte-pair-encoding (BPE), induce a sampling bias that cannot be mitigated with more training or data. To counter this universal problem, for each encoding scheme above, we propose a novel algorithm to obtain unbiased estimates from any language model trained on tokenized data. Our methods do not require finetuning the model, and the complexity, defined as the number of model runs, scales linearly with the sequence length in the case of MPE. As a result, we show that one can simulate token-free behavior from a tokenized language model. We empirically verify the correctness of our method through a Markov-chain setup, where it accurately recovers the transition probabilities, as opposed to the conventional method of directly prompting tokens into the language model.

End-to-end (E2E) keyword search (KWS) has emerged as an alternative and complimentary approach to conventional keyword search which depends on the output of automatic speech recognition (ASR) systems. While E2E methods greatly simplify the KWS pipeline, they generally have worse performance than their ASR-based counterparts, which can benefit from pretraining with untranscribed data. In this work, we propose a method for pretraining E2E KWS systems with untranscribed data, which involves using acoustic unit discovery (AUD) to obtain discrete units for untranscribed data and then learning to locate sequences of such units in the speech. We conduct experiments across languages and AUD systems: we show that finetuning such a model significantly outperforms a model trained from scratch, and the performance improvements are generally correlated with the quality of the AUD system used for pretraining.