Convergence of flow-based generative models via proximal gradient descent in Wasserstein space

Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance. Compared to the accumulating theoretical studies on related score-based diffusion models, analysis of flow-based models, which are deterministic in both forward (data-to-noise) and reverse (noise-to-data) directions, remain sparse. In this paper, we provide a theoretical guarantee of generating data distribution by a progressive flow model, the so-called JKO flow model, which implements the Jordan-Kinderleherer-Otto (JKO) scheme in a normalizing flow network. Leveraging the exponential convergence of the proximal gradient descent (GD) in Wasserstein space, we prove the Kullback-Leibler (KL) guarantee of data generation by a JKO flow model to be $O(\varepsilon^2)$ when using $N \lesssim \log (1/\varepsilon)$ many JKO steps ($N$ Residual Blocks in the flow) where $\varepsilon$ is the error in the per-step first-order condition. The assumption on data density is merely a finite second moment, and the theory extends to data distributions without density and when there are inversion errors in the reverse process where we obtain KL-$W_2$ mixed error guarantees. The non-asymptotic convergence rate of the JKO-type $W_2$-proximal GD is proved for a general class of convex objective functionals that includes the KL divergence as a special case, which can be of independent interest

Offline Policy Evaluation and Optimization under Confounding

Evaluating and optimizing policies in the presence of unobserved confounders is a problem of growing interest in offline reinforcement learning. Using conventional methods for offline RL in the presence of confounding can not only lead to poor decisions and poor policies, but can also have disastrous effects in critical applications such as healthcare and education. We map out the landscape of offline policy evaluation for confounded MDPs, distinguishing assumptions on confounding based on their time-evolution and effect on the data-collection policies. We determine when consistent value estimates are not achievable, providing and discussing algorithms to estimate lower bounds with guarantees in those cases. When consistent estimates are achievable, we provide sample complexity guarantees. We also present new algorithms for offline policy improvement and prove local convergence guarantees. Finally, we experimentally evaluate our algorithms on gridworld and a simulated healthcare setting of managing sepsis patients. We note that in gridworld, our model-based method provides tighter lower bounds than existing methods, while in the sepsis simulator, our methods significantly outperform confounder-oblivious benchmarks

Optimum Water Quality Monitoring Network Design for Bidirectional River Systems

Affected by regular tides, bidirectional water flows play a crucial role in surface river systems. Using optimization theory to design a water quality monitoring network can reduce the redundant monitoring nodes as well as save the costs for building and running a monitoring network. A novel algorithm is proposed to design an optimum water quality monitoring network for tidal rivers with bidirectional water flows. Two optimization objectives of minimum pollution detection time and maximum pollution detection probability are used in our optimization algorithm. We modify the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm and develop new fitness functions to calculate pollution detection time and pollution detection probability in a discrete manner. In addition, the Storm Water Management Model (SWMM) is used to simulate hydraulic characteristics and pollution events based on a hypothetical river system studied in the literature. Experimental results show that our algorithm can obtain a better Pareto frontier. The influence of bidirectional water flows to the network design is also identified, which has not been studied in the literature. Besides that, we also find that the probability of bidirectional water flows has no effect on the optimum monitoring network design but slightly changes the mean pollution detection time

Multimetric structural covariance in first-episode major depressive disorder: a graph theoretical analysis

Background: Abnormalities of cortical morphology have been consistently reported in major depressive disorder (MDD), with widespread focal alterations in cortical thickness, surface area and gyrification. However, it is unclear whether these distributed focal changes disrupt the system-level architecture (topology) of brain morphology in MDD. If present, such a topological disruption might explain the mechanisms that underlie altered cortical morphology in MDD. Methods: Seventy-six patients with first-episode MDD (33 male, 43 female) and 66 healthy controls (32 male, 34 female) underwent structural MRI scans. We calculated cortical indices, including cortical thickness, surface area and local gyrification index, using FreeSurfer. We constructed morphological covariance networks using the 3 cortical indices separately, and we analyzed the topological properties of these group-level morphological covariance networks using graph theoretical approaches. Results: Topological differences between patients with first-episode MDD and healthy controls were restricted to the thickness-based network. We found a significant decrease in global efficiency but an increase in local efficiency of the left superior frontal gyrus and the right paracentral lobule in patients with first-episode MDD. When we simulated targeted lesions affecting the most highly connected nodes, the thickness-based networks in patients with first-episode MDD disintegrated more rapidly than those in healthy controls. Limitations: Our sample of patients with first-episode MDD has limited generalizability to patients with chronic and recurrent MDD. Conclusion: A systems-level disruption in cortical thickness (but not surface area or gyrification) occurs in patients with first-episode MDD

Coevolutionary Diagenesis in Tight Sandstone and Shale Reservoirs within Lacustrine-Delta Systems: A Case Study from the Lianggaoshan Formation in the Eastern Sichuan Basin, Southwest China

Tight sandstone and shale oil and gas are the key targets of unconventional oil and gas exploration in the lake-delta sedimentary systems of China. Understanding the coevolutionary diagenesis of sandstone and shale reservoirs is crucial for the prediction of reservoir quality, ahead of drilling, in such systems. Thin-section description, scanning electron microscopy (SEM), X-ray diffraction (XRD), fluid inclusion analysis, porosity and permeability tests, high-pressure mercury intrusion (HPMI) measurements and nuclear magnetic resonance tests (NMR) were used to reveal the coevolutionary diagenetic mechanisms of a sandstone and shale reservoir in the Lianggaoshan Formation of the Eastern Sichuan Basin, China. The thermally mature, organic-matter-rich, dark shale of layer3 is the most important source rock within the Lianggaoshan Formation. It started to generate abundant organic acids at the early stage of mesodiagenesis and produced abundant hydrocarbons in the early Cretaceous. Porewater with high concentrations of Ca2+ and CO32− entered the sandstone reservoir from dark shale as the shale was compacted during burial. Potassium feldspar dissolution at the boundary of the sandstone was more pervasive than at the center of the sandstone. The K+ released by potassium feldspar dissolution migrated from the sandstone into mudstone. Grain-rimming chlorite coats occurred mainly in the center of the sandstone. Some silica exported from the shale was imported by the sandstone boundary and precipitated close to the shale/sandstone boundary. Some intergranular dissolution pores and intercrystal pores were formed in the shale due to dissolution during the early stages of mesodiagenesis. Chlorite coats, which precipitated during eodiagenesis, were beneficial to the protection of primary pore space in the sandstone. Calcite cement, which preferentially precipitated at the boundary of sandstone, was not conducive to reservoir development. Dissolution mainly occurred at the early stage of mesodiagenesis due to organic acids derived from the dark shale. Calcite cement could also protect some primary pores from compaction and release pore space following dissolution. The porosity of sandstone and shale was mainly controlled by the thickness of sandstone and dark shale

Designing an Optimal Water Quality Monitoring Network

Part 6: Intelligent ApplicationsInternational audienceThe optimal design of water quality monitoring network can improve the monitoring performance. In addition, it can reduce the redundant monitoring locations and save the investment and costs for building and operating the monitoring system. This paper modifies the original Multi-Objective Particle Swarm Optimization (MOPSO) to optimize the design of water quality monitoring network based on three optimization objectives: minimum pollution detection time, maximum pollution detection probability and maximum centrality of monitoring locations. We develop a new initialization procedure as well as a discrete velocity and position updating function to optimize the design of water quality monitoring network. The Storm Water Management Model (SWMM) is used to model a hypothetical river network which was studied in the literature for comparative analysis of our work. We simulate pollution events in SWMM to obtain all the pollution detection time for all the potential monitoring locations. Experimental results show that the modified MOPSO can obtain steady Pareto frontiers and better optimal deployment solutions than genetic algorithm (GA)

Prenatal selective serotonin reuptake inhibitor (SSRI) exposure induces working memory and social recognition deficits by disrupting inhibitory synaptic networks in male mice

Selective serotonin reuptake inhibitors (SSRIs) are commonly prescribed antidepressant drugs in pregnant women. Infants born following prenatal exposure to SSRIs have a higher risk for behavioral abnormalities, however, the underlying mechanisms remains unknown. Therefore, we examined the effects of prenatal fluoxetine, the most commonly prescribed SSRI, in mice. Intriguingly, chronic in utero fluoxetine treatment impaired working memory and social novelty recognition in adult males. In the medial prefrontal cortex (mPFC), a key region regulating these behaviors, we found augmented spontaneous inhibitory synaptic transmission onto the layer 5 pyramidal neurons. Fast-spiking interneurons in mPFC exhibited enhanced intrinsic excitability and serotonin-induced excitability due to upregulated serotonin (5-HT) 2A receptor (5-HT2AR) signaling. More importantly, the behavioral deficits in prenatal fluoxetine treated mice were reversed by the application of a 5-HT2AR antagonist. Taken together, our findings suggest that alterations in inhibitory neuronal modulation are responsible for the behavioral alterations following prenatal exposure to SSRIs