An important milestone for AI is the development of algorithms that can produce drawings that are indistinguishable from those of humans. Here, we adapt the 'diversity vs. recognizability' scoring framework from Boutin et al, 2022 and find that one-shot diffusion models have indeed started to close the gap between humans and machines. However, using a finer-grained measure of the originality of individual samples, we show that strengthening the guidance of diffusion models helps improve the humanness of their drawings, but they still fall short of approximating the originality and recognizability of human drawings. Comparing human category diagnostic features, collected through an online psychophysics experiment, against those derived from diffusion models reveals that humans rely on fewer and more localized features. Overall, our study suggests that diffusion models have significantly helped improve the quality of machine-generated drawings; however, a gap between humans and machines remains -- in part explainable by discrepancies in visual strategies.

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the $\varphi^4$ model and weak lensing convergence maps with higher resolution than in previous works.

We propose a policy gradient algorithm for robust infinite-horizon Markov Decision Processes (MDPs) with non-rectangular uncertainty sets, thereby addressing an open challenge in the robust MDP literature. Indeed, uncertainty sets that display statistical optimality properties and make optimal use of limited data often fail to be rectangular. Unfortunately, the corresponding robust MDPs cannot be solved with dynamic programming techniques and are in fact provably intractable. This prompts us to develop a projected Langevin dynamics algorithm tailored to the robust policy evaluation problem, which offers global optimality guarantees. We also propose a deterministic policy gradient method that solves the robust policy evaluation problem approximately, and we prove that the approximation error scales with a new measure of non-rectangularity of the uncertainty set. Numerical experiments showcase that our projected Langevin dynamics algorithm can escape local optima, while algorithms tailored to rectangular uncertainty fail to do so.

The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance. Yet, the literature on its statistical properties -- or, more accurately, its generalization properties -- with respect to the distribution of slices, beyond the uniform measure, is scarce. To bring new contributions to this line of research, we leverage the PAC-Bayesian theory and a central observation that SW may be interpreted as an average risk, the quantity PAC-Bayesian bounds have been designed to characterize. We provide three types of results: i) PAC-Bayesian generalization bounds that hold on what we refer as adaptive Sliced-Wasserstein distances, i.e. SW defined with respect to arbitrary distributions of slices (among which data-dependent distributions), ii) a principled procedure to learn the distribution of slices that yields maximally discriminative SW, by optimizing our theoretical bounds, and iii) empirical illustrations of our theoretical findings.

We study dynamic discrete choice models, where a commonly studied problem involves estimating parameters of agent reward functions (also known as "structural" parameters), using agent behavioral data. Maximum likelihood estimation for such models requires dynamic programming, which is limited by the curse of dimensionality. In this work, we present a novel algorithm that provides a data-driven method for selecting and aggregating states, which lowers the computational and sample complexity of estimation. Our method works in two stages. In the first stage, we use a flexible inverse reinforcement learning approach to estimate agent Q-functions. We use these estimated Q-functions, along with a clustering algorithm, to select a subset of states that are the most pivotal for driving changes in Q-functions. In the second stage, with these selected "aggregated" states, we conduct maximum likelihood estimation using a commonly used nested fixed-point algorithm. The proposed two-stage approach mitigates the curse of dimensionality by reducing the problem dimension. Theoretically, we derive finite-sample bounds on the associated estimation error, which also characterize the trade-off of computational complexity, estimation error, and sample complexity. We demonstrate the empirical performance of the algorithm in two classic dynamic discrete choice estimation applications.

The success of Bayesian inference with MCMC depends critically on Markov chains rapidly reaching the posterior distribution. Despite the plentitude of inferential theory for posteriors in Bayesian non-parametrics, convergence properties of MCMC algorithms that simulate from such ideal inferential targets are not thoroughly understood. This work focuses on the Bayesian CART algorithm which forms a building block of Bayesian Additive Regression Trees (BART). We derive upper bounds on mixing times for typical posteriors under various proposal distributions. Exploiting the wavelet representation of trees, we provide sufficient conditions for Bayesian CART to mix well (polynomially) under certain hierarchical connectivity restrictions on the signal. We also derive a negative result showing that Bayesian CART (based on simple grow and prune steps) cannot reach deep isolated signals in faster than exponential mixing time. To remediate myopic tree exploration, we propose Twiggy Bayesian CART which attaches/detaches entire twigs (not just single nodes) in the proposal distribution. We show polynomial mixing of Twiggy Bayesian CART without assuming that the signal is connected on a tree. Going further, we show that informed variants achieve even faster mixing. A thorough simulation study highlights discrepancies between spike-and-slab priors and Bayesian CART under a variety of proposals.

Due to the increasing adoption of electronic health records (EHR), large scale EHRs have become another rich data source for translational clinical research. Despite its potential, deriving generalizable knowledge from EHR data remains challenging. First, EHR data are generated as part of clinical care with data elements too detailed and fragmented for research. Despite recent progress in mapping EHR data to common ontology with hierarchical structures, much development is still needed to enable automatic grouping of local EHR codes to meaningful clinical concepts at a large scale. Second, the total number of unique EHR features is large, imposing methodological challenges to derive reproducible knowledge graph, especially when interest lies in conditional dependency structure. Third, the detailed EHR data on a very large patient cohort imposes additional computational challenge to deriving a knowledge network. To overcome these challenges, we propose to infer the conditional dependency structure among EHR features via a latent graphical block model (LGBM). The LGBM has a two layer structure with the first providing semantic embedding vector (SEV) representation for the EHR features and the second overlaying a graphical block model on the latent SEVs. The block structures on the graphical model also allows us to cluster synonymous features in EHR. We propose to learn the LGBM efficiently, in both statistical and computational sense, based on the empirical point mutual information matrix. We establish the statistical rates of the proposed estimators and show the perfect recovery of the block structure. Numerical results from simulation studies and real EHR data analyses suggest that the proposed LGBM estimator performs well in finite sample.

As the number of credit card users has increased, detecting fraud in this domain has become a vital issue. Previous literature has applied various supervised and unsupervised machine learning methods to find an effective fraud detection system. However, some of these methods require an enormous amount of time to achieve reasonable accuracy. In this paper, an Asexual Reproduction Optimization (ARO) approach was employed, which is a supervised method to detect credit card fraud. ARO refers to a kind of production in which one parent produces some offspring. By applying this method and sampling just from the majority class, the effectiveness of the classification is increased. A comparison to Artificial Immune Systems (AIS), which is one of the best methods implemented on current datasets, has shown that the proposed method is able to remarkably reduce the required training time and at the same time increase the recall that is important in fraud detection problems. The obtained results show that ARO achieves the best cost in a short time, and consequently, it can be considered a real-time fraud detection system.

Fairness plays a crucial role in various multi-agent systems (e.g., communication networks, financial markets, etc.). Many multi-agent dynamical interactions can be cast as Markov Decision Processes (MDPs). While existing research has focused on studying fairness in known environments, the exploration of fairness in such systems for unknown environments remains open. In this paper, we propose a Reinforcement Learning (RL) approach to achieve fairness in multi-agent finite-horizon episodic MDPs. Instead of maximizing the sum of individual agents' value functions, we introduce a fairness function that ensures equitable rewards across agents. Since the classical Bellman's equation does not hold when the sum of individual value functions is not maximized, we cannot use traditional approaches. Instead, in order to explore, we maintain a confidence bound of the unknown environment and then propose an online convex optimization based approach to obtain a policy constrained to this confidence region. We show that such an approach achieves sub-linear regret in terms of the number of episodes. Additionally, we provide a probably approximately correct (PAC) guarantee based on the obtained regret bound. We also propose an offline RL algorithm and bound the optimality gap with respect to the optimal fair solution. To mitigate computational complexity, we introduce a policy-gradient type method for the fair objective. Simulation experiments also demonstrate the efficacy of our approach.

In this paper, we consider the motion planning problem in Gaussian belief space for minimum sensing navigation. Despite the extensive use of sampling-based algorithms and their rigorous analysis in the deterministic setting, there has been little formal analysis of the quality of their solutions returned by sampling algorithms in Gaussian belief space. This paper aims to address this lack of research by examining the asymptotic behavior of the cost of solutions obtained from Gaussian belief space based sampling algorithms as the number of samples increases. To that end, we propose a sampling based motion planning algorithm termed Information Geometric PRM* (IG-PRM*) for generating feasible paths that minimize a weighted sum of the Euclidean and an information-theoretic cost and show that the cost of the solution that is returned is guaranteed to approach the global optimum in the limit of large number of samples. Finally, we consider an obstacle-free scenario and compute the optimal solution using the "move and sense" strategy in literature. We then verify that the cost returned by our proposed algorithm converges to this optimal solution as the number of samples increases.