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.

We study the design of sample-efficient algorithms for reinforcement learning in the presence of rich, high-dimensional observations, formalized via the Block MDP problem. Existing algorithms suffer from either 1) computational intractability, 2) strong statistical assumptions that are not necessarily satisfied in practice, or 3) suboptimal sample complexity. We address these issues by providing the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level, with minimal statistical assumptions. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics, a learning objective in which the aim is to predict the learner's own action from the current observation and observations in the (potentially distant) future. MusIK is simple and flexible, and can efficiently take advantage of general-purpose function approximation. Our analysis leverages several new techniques tailored to non-optimistic exploration algorithms, which we anticipate will find broader use.

We conduct the first comprehensive meta-analysis of deterministic solar forecasting based on skill score, screening 1,447 papers from Google Scholar and reviewing the full texts of 320 papers for data extraction. A database of 4,687 points was built and analyzed with multivariate adaptive regression spline modelling, partial dependence plots, and linear regression. The marginal impacts on skill score of ten factors were quantified. The analysis shows the non-linearity and complex interaction between variables in the database. Forecast horizon has a central impact and dominates other factors' impacts. Therefore, the analysis of solar forecasts should be done separately for each horizon. Climate zone variables have statistically significant correlation with skill score. Regarding inputs, historical data and spatial temporal information are highly helpful. For intra-day, sky and satellite images show the most importance. For day-ahead, numerical weather predictions and locally measured meteorological data are very efficient. All forecast models were compared. Ensemble-hybrid models achieve the most accurate forecasts for all horizons. Hybrid models show superiority for intra-hour while image-based methods are the most efficient for intra-day forecasts. More training data can enhance skill score. However, over-fitting is observed when there is too much training data (longer than 2000 days). There has been a substantial improvement in solar forecast accuracy, especially in recent years. More improvement is observed for intra-hour and intra-day than day-ahead forecasts. By controlling for the key differences between forecasts, including location variables, our findings can be applied globally.

Diffusion Models (DMs) are powerful generative models that add Gaussian noise to the data and learn to remove it. We wanted to determine which noise distribution (Gaussian or non-Gaussian) led to better generated data in DMs. Since DMs do not work by design with non-Gaussian noise, we built a framework that allows reversing a diffusion process with non-Gaussian location-scale noise. We use that framework to show that the Gaussian distribution performs the best over a wide range of other distributions (Laplace, Uniform, t, Generalized-Gaussian).

Most real-world networks evolve over time. Existing literature proposes models for dynamic networks that are either unlabeled or assumed to have a single membership structure. On the other hand, a new family of Mixed Membership Stochastic Block Models (MMSBM) allows to model static labeled networks under the assumption of mixed-membership clustering. In this work, we propose to extend this later class of models to infer dynamic labeled networks under a mixed membership assumption. Our approach takes the form of a temporal prior on the model's parameters. It relies on the single assumption that dynamics are not abrupt. We show that our method significantly differs from existing approaches, and allows to model more complex systems --dynamic labeled networks. We demonstrate the robustness of our method with several experiments on both synthetic and real-world datasets. A key interest of our approach is that it needs very few training data to yield good results. The performance gain under challenging conditions broadens the variety of possible applications of automated learning tools --as in social sciences, which comprise many fields where small datasets are a major obstacle to the introduction of machine learning methods.

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.