Lower Bounds for Two-Sample Structural Change Detection in Ising and Gaussian Models

The change detection problem is to determine if the Markov network structures of two Markov random fields differ from one another given two sets of samples drawn from the respective underlying distributions. We study the trade-off between the sample sizes and the reliability of change detection, measured as a minimax risk, for the important cases of the Ising models and the Gaussian Markov random fields restricted to the models which have network structures with $p$ nodes and degree at most $d$, and obtain information-theoretic lower bounds for reliable change detection over these models. We show that for the Ising model, $\Omega\left(\frac{d^2}{(\log d)^2}\log p\right)$ samples are required from each dataset to detect even the sparsest possible changes, and that for the Gaussian, $\Omega\left( \gamma^{-2} \log(p)\right)$ samples are required from each dataset to detect change, where $\gamma$ is the smallest ratio of off-diagonal to diagonal terms in the precision matrices of the distributions. These bounds are compared to the corresponding results in structure learning, and closely match them under mild conditions on the model parameters. Thus, our change detection bounds inherit partial tightness from the structure learning schemes in previous literature, demonstrating that in certain parameter regimes, the naive structure learning based approach to change detection is minimax optimal up to constant factors.Comment: Presented at the 55th Annual Allerton Conference on Communication, Control, and Computing, Oct. 201

Activation of mTORC1 Improves Cone Cell Metabolism and Extends Vision in Retinitis Pigmentosa Mice: A Dissertation

Retinitis Pigmentosa (RP) is an inherited photoreceptor degenerative disease that leads to blindness and affects about 1 in 4000 people worldwide. The disease is predominantly caused by mutations in genes expressed exclusively in the night active rod photoreceptors; however, blindness results from the secondary loss of the day active cone photoreceptors, the mechanism of which remains elusive. Here, we show that the mammalian target of rapamycin complex 1 (mTORC1) is required to delay the progression of cone death during disease and that constitutive activation of mTORC1 is sufficient to maintain cone function and promote cone survival in RP. Activation of mTORC1 increased expression of genes that promote glucose uptake, retention and utilization, leading to increased NADPH levels; a key metabolite for cones. This protective effect was conserved in two mouse models of RP, indicating that the secondary loss of cones can be delayed by an approach that is independent of the primary mutation in rods. However, since mTORC1 is a negative regulator of autophagy, its constitutive activation led to an unwarranted secondary effect of shortage of amino acids due to incomplete digestion of autophagic cargo, which reduces the efficiency of cone survival over time. Moderate activation of mTORC1, which promotes expression of glycolytic genes, as well as maintains autophagy, provided more sustained cone survival. Together, our work addresses a long-standing question of non-autonomous cone death in RP and presents a novel, mutation-independent approach to extend vision in a disease that remains incurable

Doubly-Optimistic Play for Safe Linear Bandits

The safe linear bandit problem (SLB) is an online approach to linear programming with unknown objective and unknown round-wise constraints, under stochastic bandit feedback of rewards and safety risks of actions. We study aggressive \emph{doubly-optimistic play} in SLBs, and their role in avoiding the strong assumptions and poor efficacy associated with extant pessimistic-optimistic solutions. We first elucidate an inherent hardness in SLBs due the lack of knowledge of constraints: there exist `easy' instances, for which suboptimal extreme points have large `gaps', but on which SLB methods must still incur $\Omega(\sqrt{T})$ regret and safety violations due to an inability to refine the location of optimal actions to arbitrary precision. In a positive direction, we propose and analyse a doubly-optimistic confidence-bound based strategy for the safe linear bandit problem, DOSLB, which exploits supreme optimism by using optimistic estimates of both reward and safety risks to select actions. Using a novel dual analysis, we show that despite the lack of knowledge of constraints, DOSLB rarely takes overly risky actions, and obtains tight instance-dependent $O(\log^2 T)$ bounds on both efficacy regret and net safety violations up to any finite precision, thus yielding large efficacy gains at a small safety cost and without strong assumptions. Concretely, we argue that algorithm activates noisy versions of an `optimal' set of constraints at each round, and activation of suboptimal sets of constraints is limited by the larger of a safety and efficacy gap we define.Comment: v2: extensive rewrite, with a much cleaner exposition of the theory, and improvements in key definition

Strategies for Safe Multi-Armed Bandits with Logarithmic Regret and Risk

We investigate a natural but surprisingly unstudied approach to the multi-armed bandit problem under safety risk constraints. Each arm is associated with an unknown law on safety risks and rewards, and the learner's goal is to maximise reward whilst not playing unsafe arms, as determined by a given threshold on the mean risk. We formulate a pseudo-regret for this setting that enforces this safety constraint in a per-round way by softly penalising any violation, regardless of the gain in reward due to the same. This has practical relevance to scenarios such as clinical trials, where one must maintain safety for each round rather than in an aggregated sense. We describe doubly optimistic strategies for this scenario, which maintain optimistic indices for both safety risk and reward. We show that schema based on both frequentist and Bayesian indices satisfy tight gap-dependent logarithmic regret bounds, and further that these play unsafe arms only logarithmically many times in total. This theoretical analysis is complemented by simulation studies demonstrating the effectiveness of the proposed schema, and probing the domains in which their use is appropriate

Loss of the cone-enriched caspase-7 does not affect secondary cone death in retinitis pigmentosa

Purpose: The apoptotic mechanisms responsible for secondary cone death in retinitis pigmentosa (RP) remain largely unknown. The cone-enriched apoptotic protease caspase-7 (Casp7) is thought to be triggered by endoplasmic reticulum (ER) stress and plays a pivotal role in mice deficient in the cone cyclic nucleotide-gated channels, a deficiency that causes achromatopsia in humans and in mice with autosomal dominant rhodopsin mutations, in particular the T17M mutation. Thus, we tested in two mouse models of RP whether the cone-enriched Casp7 plays a role during secondary cone death. Methods: Casp7 knockout mice were crossed to two different RP mouse models with significantly different rod and cone death kinetics: the rd1 mouse model, which carries a mutation in the Pde6b gene, and the rhodopsin knockout mouse model (Rho-KO or Rho(-/-) ). In both models, cone survival was assessed on retinal flat mounts by quantifying the percentage of cone arrestin staining over the retinal surface area. The analyses were performed at two different time points for each model. Results: Loss of Casp7 did not alter cone survival in either of the two mouse models tested regardless of the time point analyzed. Rod survival was also not affected in either model nor did loss of Casp7 affect rod or cone function in a wild-type background as assessed with electroretinogram analyses. Conclusions: Secondary cone death in retinitis pigmentosa is unlikely to be triggered by ER stress and is likely independent of Casp7 activity