Optogenetics is widely used to study the effects of neural circuit manipulation on behavior. However, the paucity of causal inference methodological work on this topic has resulted in analysis conventions that discard information, and constrain the scientific questions that can be posed. To fill this gap, we introduce a nonparametric causal inference framework for analyzing "closed-loop" designs, which use dynamic policies that assign treatment based on covariates. In this setting, standard methods can introduce bias and occlude causal effects. Building on the sequentially randomized experiments literature in causal inference, our approach extends history-restricted marginal structural models for dynamic regimes. In practice, our framework can identify a wide range of causal effects of optogenetics on trial-by-trial behavior, such as, fast/slow-acting, dose-response, additive/antagonistic, and floor/ceiling. Importantly, it does so without requiring negative controls, and can estimate how causal effect magnitudes evolve across time points. From another view, our work extends "excursion effect" methods--popular in the mobile health literature--to enable estimation of causal contrasts for treatment sequences greater than length one, in the presence of positivity violations. We derive rigorous statistical guarantees, enabling hypothesis testing of these causal effects. We demonstrate our approach on data from a recent study of dopaminergic activity on learning, and show how our method reveals relevant effects obscured in standard analyses.
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We consider the problem of approximating an unknown function in a nonlinear model class from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial. Recently, an increasing focus has been on employing adaptive sampling strategies to achieve this. These strategies are based on linear spaces related to the nonlinear model class, for which the optimal sampling measures are known. However, the resulting optimal sampling measures depend on an orthonormal basis of the linear space, which is known rarely. Consequently, sampling from these measures is challenging in practice. This manuscript presents a sampling strategy that iteratively refines an estimate of the optimal sampling measure by updating it based on previously drawn samples. This strategy can be performed offline and does not require evaluations of the sought function. We establish convergence and illustrate the practical performance through numerical experiments. Comparing the presented approach with standard Monte Carlo sampling demonstrates a significant reduction in the number of samples required to achieve a good estimation of an orthonormal basis.
We propose a topological mapping and localization system able to operate on real human colonoscopies, despite significant shape and illumination changes. The map is a graph where each node codes a colon location by a set of real images, while edges represent traversability between nodes. For close-in-time images, where scene changes are minor, place recognition can be successfully managed with the recent transformers-based local feature matching algorithms. However, under long-term changes -- such as different colonoscopies of the same patient -- feature-based matching fails. To address this, we train on real colonoscopies a deep global descriptor achieving high recall with significant changes in the scene. The addition of a Bayesian filter boosts the accuracy of long-term place recognition, enabling relocalization in a previously built map. Our experiments show that ColonMapper is able to autonomously build a map and localize against it in two important use cases: localization within the same colonoscopy or within different colonoscopies of the same patient. Code: //github.com/jmorlana/ColonMapper.
Analyzing longitudinal data in health studies is challenging due to sparse and error-prone measurements, strong within-individual correlation, missing data and various trajectory shapes. While mixed-effect models (MM) effectively address these challenges, they remain parametric models and may incur computational costs. In contrast, Functional Principal Component Analysis (FPCA) is a non-parametric approach developed for regular and dense functional data that flexibly describes temporal trajectories at a potentially lower computational cost. This paper presents an empirical simulation study evaluating the behaviour of FPCA with sparse and error-prone repeated measures and its robustness under different missing data schemes in comparison with MM. The results show that FPCA is well-suited in the presence of missing at random data caused by dropout, except in scenarios involving most frequent and systematic dropout. Like MM, FPCA fails under missing not at random mechanism. The FPCA was applied to describe the trajectories of four cognitive functions before clinical dementia and contrast them with those of matched controls in a case-control study nested in a population-based aging cohort. The average cognitive declines of future dementia cases showed a sudden divergence from those of their matched controls with a sharp acceleration 5 to 2.5 years prior to diagnosis.
A new approach based on censoring and moment criterion is introduced for parameter estimation of count distributions when the probability generating function is available even though a closed form of the probability mass function and/or finite moments do not exist.
The purpose of the study was to find the true comfort of the wearer by conceptualizing, formulating, and proving the relation between physiological and emotional parameters with clothing fit and fabric. A mixed-method research design was used, and the findings showed that physiological indicators such as heart rate are closely linked with user comfort. However, a significant change in emotional response indicated a definite relationship between different fabric and fit types. The research was conducted to discover the relation between true comfort parameters and clothing, which is unique to the field. The findings help us understand how fabric types and clothing fit types can affect physiological and emotional responses, providing the consumer with satisfactory clothing with the suitable properties needed.
Finding the optimal design of experiments in the Bayesian setting typically requires estimation and optimization of the expected information gain functional. This functional consists of one outer and one inner integral, separated by the logarithm function applied to the inner integral. When the mathematical model of the experiment contains uncertainty about the parameters of interest and nuisance uncertainty, (i.e., uncertainty about parameters that affect the model but are not themselves of interest to the experimenter), two inner integrals must be estimated. Thus, the already considerable computational effort required to determine good approximations of the expected information gain is increased further. The Laplace approximation has been applied successfully in the context of experimental design in various ways, and we propose two novel estimators featuring the Laplace approximation to alleviate the computational burden of both inner integrals considerably. The first estimator applies Laplace's method followed by a Laplace approximation, introducing a bias. The second estimator uses two Laplace approximations as importance sampling measures for Monte Carlo approximations of the inner integrals. Both estimators use Monte Carlo approximation for the remaining outer integral estimation. We provide four numerical examples demonstrating the applicability and effectiveness of our proposed estimators.
We obtain the almost sure strong consistency and the Berry-Esseen type bound for the maximum likelihood estimator Ln of the ensemble L for determinantal point processes (DPPs), strengthening and completing previous work initiated in Brunel, Moitra, Rigollet, and Urschel [BMRU17]. Numerical algorithms of estimating DPPs are developed and simulation studies are performed. Lastly, we give explicit formula and a detailed discussion for the maximum likelihood estimator for blocked determinantal matrix of two by two submatrices and compare it with the frequency method.
Shape-restricted inferences have exhibited empirical success in various applications with survival data. However, certain works fall short in providing a rigorous theoretical justification and an easy-to-use variance estimator with theoretical guarantee. Motivated by Deng et al. (2023), this paper delves into an additive and shape-restricted partially linear Cox model for right-censored data, where each additive component satisfies a specific shape restriction, encompassing monotonic increasing/decreasing and convexity/concavity. We systematically investigate the consistencies and convergence rates of the shape-restricted maximum partial likelihood estimator (SMPLE) of all the underlying parameters. We further establish the aymptotic normality and semiparametric effiency of the SMPLE for the linear covariate shift. To estimate the asymptotic variance, we propose an innovative data-splitting variance estimation method that boasts exceptional versatility and broad applicability. Our simulation results and an analysis of the Rotterdam Breast Cancer dataset demonstrate that the SMPLE has comparable performance with the maximum likelihood estimator under the Cox model when the Cox model is correct, and outperforms the latter and Huang (1999)'s method when the Cox model is violated or the hazard is nonsmooth. Meanwhile, the proposed variance estimation method usually leads to reliable interval estimates based on the SMPLE and its competitors.
In the analysis of spatially resolved transcriptomics data, detecting spatially variable genes (SVGs) is crucial. Numerous computational methods exist, but varying SVG definitions and methodologies lead to incomparable results. We review 31 state-of-the-art methods, categorizing SVGs into three types: overall, cell-type-specific, and spatial-domain-marker SVGs. Our review explains the intuitions underlying these methods, summarizes their applications, and categorizes the hypothesis tests they use in the trade-off between generality and specificity for SVG detection. We discuss challenges in SVG detection and propose future directions for improvement. Our review offers insights for method developers and users, advocating for category-specific benchmarking.
We investigate the set of invariant idempotent probabilities for countable idempotent iterated function systems (IFS) defined in compact metric spaces. We demonstrate that, with constant weights, there exists a unique invariant idempotent probability. Utilizing Secelean's approach to countable IFSs, we introduce partially finite idempotent IFSs and prove that the sequence of invariant idempotent measures for these systems converges to the invariant measure of the original countable IFS. We then apply these results to approximate such measures with discrete systems, producing, in the one-dimensional case, data series whose Higuchi fractal dimension can be calculated. Finally, we provide numerical approximations for two-dimensional cases and discuss the application of generalized Higuchi dimensions in these scenarios.
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