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.

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.

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.

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.

Their use as a decision support tool in business and OR has been increasing over the years, including case studies in project management (van Dorp, 2020), supply chain (Garvey et al., 2015), marketing (Hosseini, 2021), and logistics (Qazi, 2022), among others. BNs are defined by two components: a directed acyclic graph (DAG) where each node is a variable of interest and edges represent the, possibly causal, relationship between them; a conditional probability table (CPT) for each node of the DAG reporting the probability distribution of the associated variable conditional on its parents. BNs are highly interpretable due to their graphical nature, representing the probabilistic relationships between variables, making it easy for users to understand and trace the influence of one variable on another. With explainability now recognized as critical for the use of AI in applied research (Rudin, 2019), including in OR (De Bock et al., 2023), BNs stand out by providing transparent and intuitive explanations, thereby enhancing trust and clarity in decision-making processes. The underlying DAG and the associated CPTs can be learned from data using machine learning algorithms or elicited using experts' opinions and knowledge. There is now a vast amount of algorithms to learn BN from data (e.g.

This paper proposes a novel fast online methodology for outlier detection called the exception maximization outlier detection method(EMODM), which employs probabilistic models and statistical algorithms to detect abnormal patterns from the outputs of complex systems. The EMODM is based on a two-state Gaussian mixture model and demonstrates strong performance in probability anomaly detection working on real-time raw data rather than using special prior distribution information. We confirm this using the synthetic data from two numerical cases. For the real-world data, we have detected the short circuit pattern of the circuit system using EMODM by the current and voltage output of a three-phase inverter. The EMODM also found an abnormal period due to COVID-19 in the insured unemployment data of 53 regions in the United States from 2000 to 2024. The application of EMODM to these two real-life datasets demonstrated the effectiveness and accuracy of our algorithm.

In this paper, we will introduce a novel deep model named Reconciled Polynomial Network (RPN) for deep function learning. RPN has a very general architecture and can be used to build models with various complexities, capacities, and levels of completeness, which all contribute to the correctness of these models. As indicated in the subtitle, RPN can also serve as the backbone to unify different base models into one canonical representation. This includes non-deep models, like probabilistic graphical models (PGMs) - such as Bayesian network and Markov network - and kernel support vector machines (kernel SVMs), as well as deep models like the classic multi-layer perceptron (MLP) and the recent Kolmogorov-Arnold network (KAN). Technically, RPN proposes to disentangle the underlying function to be inferred into the inner product of a data expansion function and a parameter reconciliation function. Together with the remainder function, RPN accurately approximates the underlying functions that governs data distributions. The data expansion functions in RPN project data vectors from the input space to a high-dimensional intermediate space, specified by the expansion functions in definition. Meanwhile, RPN also introduces the parameter reconciliation functions to fabricate a small number of parameters into a higher-order parameter matrix to address the ``curse of dimensionality'' problem caused by the data expansions. Moreover, the remainder functions provide RPN with additional complementary information to reduce potential approximation errors. We conducted extensive empirical experiments on numerous benchmark datasets across multiple modalities, including continuous function datasets, discrete vision and language datasets, and classic tabular datasets, to investigate the effectiveness of RPN.

Recent years have witnessed a growing call for renewed emphasis on neuroscience-inspired approaches in artificial intelligence research, under the banner of $\textit{NeuroAI}$. This is exemplified by recent attention gained by predictive coding networks (PCNs) within machine learning (ML). PCNs are based on the neuroscientific framework of predictive coding (PC), which views the brain as a hierarchical Bayesian inference model that minimizes prediction errors from feedback connections. PCNs trained with inference learning (IL) have potential advantages to traditional feedforward neural networks (FNNs) trained with backpropagation. While historically more computationally intensive, recent improvements in IL have shown that it can be more efficient than backpropagation with sufficient parallelization, making PCNs promising alternatives for large-scale applications and neuromorphic hardware. Moreover, PCNs can be mathematically considered as a superset of traditional FNNs, which substantially extends the range of possible architectures for both supervised and unsupervised learning. In this work, we provide a comprehensive review as well as a formal specification of PCNs, in particular placing them in the context of modern ML methods, and positioning PC as a versatile and promising framework worthy of further study by the ML community.

Large Language Models (LLMs) vary in their abilities on a range of tasks. Initiatives such as the $\texttt{Open LLM Leaderboard}$ aim to quantify these differences with several large benchmarks (sets of test items to which an LLM can respond either correctly or incorrectly). However, high correlations within and between benchmark scores suggest that (1) there exists a small set of common underlying abilities that these benchmarks measure, and (2) items tap into redundant information and the benchmarks may thus be considerably compressed. We use data from $n > 5000$ LLMs to identify the most informative items of six benchmarks, ARC, GSM8K, HellaSwag, MMLU, TruthfulQA and WinoGrande (with $d=28,632$ items in total). From them we distill a sparse benchmark, $\texttt{metabench}$, that has less than $3\%$ of the original size of all six benchmarks combined. This new sparse benchmark goes beyond point scores by yielding estimators of the underlying benchmark-specific abilities. We show that these estimators (1) can be used to reconstruct each original $\textit{individual}$ benchmark score with, on average, $1.5\%$ root mean square error (RMSE), (2) reconstruct the original $\textit{total}$ score with $0.8\%$ RMSE, and (3) have a single underlying common factor whose Spearman correlation with the total score is $r = 0.93$.