Dynamics of Coordinate Ascent Variational Inference: A Case Study in 2D Ising Models.

Variational algorithms have gained prominence over the past two decades as a scalable computational environment for Bayesian inference. In this article, we explore tools from the dynamical systems literature to study the convergence of coordinate ascent algorithms for mean field variational inference. Focusing on the Ising model defined on two nodes, we fully characterize the dynamics of the sequential coordinate ascent algorithm and its parallel version. We observe that in the regime where the objective function is convex, both the algorithms are stable and exhibit convergence to the unique fixed point. Our analyses reveal interesting discordances between these two versions of the algorithm in the region when the objective function is non-convex. In fact, the parallel version exhibits a periodic oscillatory behavior which is absent in the sequential version. Drawing intuition from the Markov chain Monte Carlo literature, we empirically show that a parameter expansion of the Ising model, popularly called the Edward-Sokal coupling, leads to an enlargement of the regime of convergence to the global optima.

VISTA Deficiency Accelerates the Development of Fatal Murine Lupus Nephritis.

OBJECTIVE: The targeting of negative checkpoint regulators as a means of augmenting antitumor immune responses is now an increasingly used and remarkably effective approach to the treatment of several human malignancies. The negative checkpoint regulator VISTA (V-domain Ig-containing suppressor of T cell activation; also known as programmed death 1 homolog or as death domain 1α) suppresses T cell responses and regulates myeloid activities. We proposed that exploitation of the VISTA pathway is a novel strategy for the treatment of human autoimmune disease, and therefore we undertook this study to determine the impact of VISTA genetic deficiency on lupus development in a lupus-prone mouse strain. METHODS: To evaluate whether genetic deficiency of VISTA affects the development of lupus, we interbred VISTA-deficient mice with Sle1.Sle3 mice, a well-characterized model of systemic lupus erythematosus (SLE). RESULTS: We demonstrated that the development of proteinuria and glomerulonephritis in these mice, designated Sle1.Sle3 VISTA-/- mice, was greatly accelerated and more severe compared to that in Sle1.Sle3 and C57BL/6 VISTA-/- mice. Analysis of cells from Sle1.Sle3 VISTA-/- mice showed enhanced activation of splenic CD4+ T cells and myeloid cell populations. No increase in titers of autoantibodies was seen in Sle1.Sle3 VISTA-/- mice. Most striking was a significant increase in proinflammatory cytokines, chemokines, and interferon (IFN)-regulated genes associated with SLE, such as IFNα, IFNγ, tumor necrosis factor, interleukin-10, and CXCL10, in Sle1.Sle3 VISTA-/- mice. CONCLUSION: This study demonstrates for the first time that loss of VISTA in murine SLE exacerbates disease due to enhanced myeloid and T cell activation and cytokine production, including a robust IFNα signature, and supports a strategy of enhancement of the immunosuppressive activity of VISTA for the treatment of human lupus.