Biochemical reaction networks are an amalgamation of reactions where each reaction represents the interaction of different species. Generally, these networks exhibit a multi-scale behavior caused by the high variability in reaction rates and abundances of species. The so-called jump-diffusion approximation is a valuable tool in the modeling of such systems. The approximation is constructed by partitioning the reaction network into a fast and slow subgroup of fast and slow reactions, respectively. This enables the modeling of the dynamics using a Langevin equation for the fast group, while a Markov jump process model is kept for the dynamics of the slow group. Most often biochemical processes are poorly characterized in terms of parameters and population states. As a result of this, methods for estimating hidden quantities are of significant interest. In this paper, we develop a tractable Bayesian inference algorithm based on Markov chain Monte Carlo. The presented blocked Gibbs particle smoothing algorithm utilizes a sequential Monte Carlo method to estimate the latent states and performs distinct Gibbs steps for the parameters of a biochemical reaction network, by exploiting a jump-diffusion approximation model. The presented blocked Gibbs sampler is based on the two distinct steps of state inference and parameter inference. We estimate states via a continuous-time forward-filtering backward-smoothing procedure in the state inference step. By utilizing bootstrap particle filtering within a backward-smoothing procedure, we sample a smoothing trajectory. For estimating the hidden parameters, we utilize a separate Markov chain Monte Carlo sampler within the Gibbs sampler that uses the path-wise continuous-time representation of the reaction counters. Finally, the algorithm is numerically evaluated for a partially observed multi-scale birth-death process example.

In a randomized exam, each student is asked a small number of random questions from a large question bank. The predominant grading rule is simple averaging, i.e., calculating grades by averaging scores on the questions each student is asked, which is fair ex-ante, over the randomized questions, but not fair ex-post, on the realized questions. The fair grading problem is to estimate the average grade of each student on the full question bank. The maximum-likelihood estimator for the Bradley-Terry-Luce model on the bipartite student-question graph is shown to be consistent with high probability when the number of questions asked to each student is at least the cubed-logarithm of the number of students. In an empirical study on exam data and in simulations, our algorithm based on the maximum-likelihood estimator significantly outperforms simple averaging in prediction accuracy and ex-post fairness even with a small class and exam size.

Learning image classification and image generation using the same set of network parameters is a challenging problem. Recent advanced approaches perform well in one task often exhibit poor performance in the other. This work introduces an energy-based classifier and generator, namely EGC, which can achieve superior performance in both tasks using a single neural network. Unlike a conventional classifier that outputs a label given an image (i.e., a conditional distribution $p(y|\mathbf{x})$), the forward pass in EGC is a classifier that outputs a joint distribution $p(\mathbf{x},y)$, enabling an image generator in its backward pass by marginalizing out the label $y$. This is done by estimating the energy and classification probability given a noisy image in the forward pass, while denoising it using the score function estimated in the backward pass. EGC achieves competitive generation results compared with state-of-the-art approaches on ImageNet-1k, CelebA-HQ and LSUN Church, while achieving superior classification accuracy and robustness against adversarial attacks on CIFAR-10. This work represents the first successful attempt to simultaneously excel in both tasks using a single set of network parameters. We believe that EGC bridges the gap between discriminative and generative learning.

Knowledge graphs (KGs) have attracted more and more attentions because of their fundamental roles in many tasks. Quality evaluation for KGs is thus crucial and indispensable. Existing methods in this field evaluate KGs by either proposing new quality metrics from different dimensions or measuring performances at KG construction stages. However, there are two major issues with those methods. First, they highly rely on raw data in KGs, which makes KGs' internal information exposed during quality evaluation. Second, they consider more about the quality at data level instead of ability level, where the latter one is more important for downstream applications. To address these issues, we propose a knowledge graph quality evaluation framework under incomplete information (QEII). The quality evaluation task is transformed into an adversarial Q&A game between two KGs. Winner of the game is thus considered to have better qualities. During the evaluation process, no raw data is exposed, which ensures information protection. Experimental results on four pairs of KGs demonstrate that, compared with baselines, the QEII implements a reasonable quality evaluation at ability level under incomplete information.

This paper considers the problem of testing the maximum in-degree of the Bayes net underlying an unknown probability distribution $P$ over $\{0,1\}^n$, given sample access to $P$. We show that the sample complexity of the problem is $\tilde{\Theta}(2^{n/2}/\varepsilon^2)$. Our algorithm relies on a testing-by-learning framework, previously used to obtain sample-optimal testers; in order to apply this framework, we develop new algorithms for ``near-proper'' learning of Bayes nets, and high-probability learning under $\chi^2$ divergence, which are of independent interest.

We consider modeling a binary response variable together with a set of covariates for two groups under observational data. The grouping variable can be the confounding variable (the common cause of treatment and outcome), gender, case/control, ethnicity, etc. Given the covariates and a binary latent variable, the goal is to construct two directed acyclic graphs (DAGs), while sharing some common parameters. The set of nodes, which represent the variables, are the same for both groups but the directed edges between nodes, which represent the causal relationships between the variables, can be potentially different. For each group, we also estimate the effect size for each node. We assume that each group follows a Gaussian distribution under its DAG. Given the parent nodes, the joint distribution of DAG is conditionally independent due to the Markov property of DAGs. We introduce the concept of Gaussian DAG-probit model under two groups and hence doubly Gaussian DAG-probit model. To estimate the skeleton of the DAGs and the model parameters, we took samples from the posterior distribution of doubly Gaussian DAG-probit model via MCMC method. We validated the proposed method using a comprehensive simulation experiment and applied it on two real datasets. Furthermore, we validated the results of the real data analysis using well-known experimental studies to show the value of the proposed grouping variable in the causality domain.

Meta-learning is a framework for learning learning algorithms through repeated interactions with an environment as opposed to designing them by hand. In recent years, this framework has established itself as a promising tool for building models of human cognition. Yet, a coherent research program around meta-learned models of cognition is still missing. The purpose of this article is to synthesize previous work in this field and establish such a research program. We rely on three key pillars to accomplish this goal. We first point out that meta-learning can be used to construct Bayes-optimal learning algorithms. This result not only implies that any behavioral phenomenon that can be explained by a Bayesian model can also be explained by a meta-learned model but also allows us to draw strong connections to the rational analysis of cognition. We then discuss several advantages of the meta-learning framework over traditional Bayesian methods. In particular, we argue that meta-learning can be applied to situations where Bayesian inference is impossible and that it enables us to make rational models of cognition more realistic, either by incorporating limited computational resources or neuroscientific knowledge. Finally, we reexamine prior studies from psychology and neuroscience that have applied meta-learning and put them into the context of these new insights. In summary, our work highlights that meta-learning considerably extends the scope of rational analysis and thereby of cognitive theories more generally.

We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear equations for tensor cores in this tensor network. The complexity of the resulting algorithm scales linearly in the dimension of the high-dimensional density. An analysis of estimation error demonstrates the effectiveness of this method through several numerical experiments.

Learning causal relationships solely from observational data provides insufficient information about the underlying causal mechanism and the search space of possible causal graphs. As a result, often the search space can grow exponentially for approaches such as Greedy Equivalence Search (GES) that uses a score-based approach to search the space of equivalence classes of graphs. Prior causal information such as the presence or absence of a causal edge can be leveraged to guide the discovery process towards a more restricted and accurate search space. In this study, we present KGS, a knowledge-guided greedy score-based causal discovery approach that uses observational data and structural priors (causal edges) as constraints to learn the causal graph. KGS is a novel application of knowledge constraints that can leverage any of the following prior edge information between any two variables: the presence of a directed edge, the absence of an edge, and the presence of an undirected edge. We extensively evaluate KGS across multiple settings in both synthetic and benchmark real-world datasets. Our experimental results demonstrate that structural priors of any type and amount are helpful and guide the search process towards an improved performance and early convergence.

Conditional randomization tests (CRTs) assess whether a variable $x$ is predictive of another variable $y$, having observed covariates $z$. CRTs require fitting a large number of predictive models, which is often computationally intractable. Existing solutions to reduce the cost of CRTs typically split the dataset into a train and test portion, or rely on heuristics for interactions, both of which lead to a loss in power. We propose the decoupled independence test (DIET), an algorithm that avoids both of these issues by leveraging marginal independence statistics to test conditional independence relationships. DIET tests the marginal independence of two random variables: $F(x \mid z)$ and $F(y \mid z)$ where $F(\cdot \mid z)$ is a conditional cumulative distribution function (CDF). These variables are termed "information residuals." We give sufficient conditions for DIET to achieve finite sample type-1 error control and power greater than the type-1 error rate. We then prove that when using the mutual information between the information residuals as a test statistic, DIET yields the most powerful conditionally valid test. Finally, we show DIET achieves higher power than other tractable CRTs on several synthetic and real benchmarks.