A design-based individual prediction approach is developed based on the expected cross-validation results, given the sampling design and the sample-splitting design for cross-validation. Whether the predictor is selected from an ensemble of models or a weighted average of them, valid inference of the unobserved prediction errors is defined and obtained with respect to the sampling design, while outcomes and features are treated as constants.
Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single point solution and propose a probabilistic paradigm to estimate a diverse set of counterfactuals. Specifically, we treat the perturbations as random variables endowed with prior distribution functions. This allows sampling multiple counterfactuals from the posterior density, with the added benefit of incorporating inductive biases, preserving domain specific constraints and quantifying uncertainty in estimates. More importantly, we leverage Bayesian hierarchical modeling to share information across different subgroups of a population, which can both improve robustness and measure fairness. A gradient based sampler with superior convergence characteristics efficiently computes the posterior samples. Experiments across several datasets demonstrate that the counterfactuals estimated using our approach are valid, sparse, diverse and feasible.
Prediction-powered inference is a framework for performing valid statistical inference when an experimental dataset is supplemented with predictions from a machine-learning system. The framework yields simple algorithms for computing provably valid confidence intervals for quantities such as means, quantiles, and linear and logistic regression coefficients, without making any assumptions on the machine-learning algorithm that supplies the predictions. Furthermore, more accurate predictions translate to smaller confidence intervals. Prediction-powered inference could enable researchers to draw valid and more data-efficient conclusions using machine learning. The benefits of prediction-powered inference are demonstrated with datasets from proteomics, astronomy, genomics, remote sensing, census analysis, and ecology.
We consider the problem of evaluating the performance of a decision policy using past observational data. The outcome of a policy is measured in terms of a loss (aka. disutility or negative reward) and the main problem is making valid inferences about its out-of-sample loss when the past data was observed under a different and possibly unknown policy. Using a sample-splitting method, we show that it is possible to draw such inferences with finite-sample coverage guarantees about the entire loss distribution, rather than just its mean. Importantly, the method takes into account model misspecifications of the past policy - including unmeasured confounding. The evaluation method can be used to certify the performance of a policy using observational data under a specified range of credible model assumptions.
Recently, Optical wireless communication (OWC) have been considered as a key element in the next generation of wireless communications due to its potential in supporting unprecedented communication speeds. In this paper, infrared lasers referred to as vertical-cavity surface-emitting lasers (VCSELs) are used as transmitters sending information to multiple users. In OWC, rate-maximization optimization problems are usually complex due to the high number of optical access points (APs) needed to ensure coverage. Therefore, practical solutions with low computational time are essential to cope with frequent updates in user-requirements that might occur. In this context, we formulate an optimization problem to determine the optimal user association and resource allocation in the network, while the serving time is partitioned into a series of time periods. Therefore, cooperative ANN models are designed to estimate and predict the association and resource allocation variables for each user such that sub-optimal solutions can be obtained within a certain period of time prior to its actual starting, which makes the solutions valid and in accordance with the demands of the users at a given time. The results show the effectiveness of the proposed model in maximizing the sum rate of the network compared with counterpart models. Moreover, ANN-based solutions are close to the optimal ones with low computational time.
This paper studies the causal representation learning problem when the latent causal variables are observed indirectly through an unknown linear transformation. The objectives are: (i) recovering the unknown linear transformation (up to scaling) and (ii) determining the directed acyclic graph (DAG) underlying the latent variables. Sufficient conditions for DAG recovery are established, and it is shown that a large class of non-linear models in the latent space (e.g., causal mechanisms parameterized by two-layer neural networks) satisfy these conditions. These sufficient conditions ensure that the effect of an intervention can be detected correctly from changes in the score. Capitalizing on this property, recovering a valid transformation is facilitated by the following key property: any valid transformation renders latent variables' score function to necessarily have the minimal variations across different interventional environments. This property is leveraged for perfect recovery of the latent DAG structure using only \emph{soft} interventions. For the special case of stochastic \emph{hard} interventions, with an additional hypothesis testing step, one can also uniquely recover the linear transformation up to scaling and a valid causal ordering.
Recovering full 3D shapes from partial observations is a challenging task that has been extensively addressed in the computer vision community. Many deep learning methods tackle this problem by training 3D shape generation networks to learn a prior over the full 3D shapes. In this training regime, the methods expect the inputs to be in a fixed canonical form, without which they fail to learn a valid prior over the 3D shapes. We propose SCARP, a model that performs Shape Completion in ARbitrary Poses. Given a partial pointcloud of an object, SCARP learns a disentangled feature representation of pose and shape by relying on rotationally equivariant pose features and geometric shape features trained using a multi-tasking objective. Unlike existing methods that depend on an external canonicalization, SCARP performs canonicalization, pose estimation, and shape completion in a single network, improving the performance by 45% over the existing baselines. In this work, we use SCARP for improving grasp proposals on tabletop objects. By completing partial tabletop objects directly in their observed poses, SCARP enables a SOTA grasp proposal network improve their proposals by 71.2% on partial shapes. Project page: https://bipashasen.github.io/scarp
Plausible identification of conditional average treatment effects (CATEs) may rely on controlling for a large number of variables to account for confounding factors. In these high-dimensional settings, estimation of the CATE requires estimating first-stage models whose consistency relies on correctly specifying their parametric forms. While doubly-robust estimators of the CATE exist, inference procedures based on the second stage CATE estimator are not doubly-robust. Using the popular augmented inverse propensity weighting signal, we propose an estimator for the CATE whose resulting Wald-type confidence intervals are doubly-robust. We assume a logistic model for the propensity score and a linear model for the outcome regression, and estimate the parameters of these models using an $\ell_1$ (Lasso) penalty to address the high dimensional covariates. Our proposed estimator remains consistent at the nonparametric rate and our proposed pointwise and uniform confidence intervals remain asymptotically valid even if one of the logistic propensity score or linear outcome regression models are misspecified. These results are obtained under similar conditions to existing analyses in the high-dimensional and nonparametric literatures.
In this paper, I try to tame "Basu's elephants" (data with extreme selection on observables). I propose new practical large-sample and finite-sample methods for estimating and inferring heterogeneous causal effects (under unconfoundedness) in the empirically relevant context of limited overlap. I develop a general principle called "Stable Probability Weighting" (SPW) that can be used as an alternative to the widely used Inverse Probability Weighting (IPW) technique, which relies on strong overlap. I show that IPW (or its augmented version), when valid, is a special case of the more general SPW (or its doubly robust version), which adjusts for the extremeness of the conditional probabilities of the treatment states. The SPW principle can be implemented using several existing large-sample parametric, semiparametric, and nonparametric procedures for conditional moment models. In addition, I provide new finite-sample results that apply when unconfoundedness is plausible within fine strata. Since IPW estimation relies on the problematic reciprocal of the estimated propensity score, I develop a "Finite-Sample Stable Probability Weighting" (FPW) set-estimator that is unbiased in a sense. I also propose new finite-sample inference methods for testing a general class of weak null hypotheses. The associated computationally convenient methods, which can be used to construct valid confidence sets and to bound the finite-sample confidence distribution, are of independent interest. My large-sample and finite-sample frameworks extend to the setting of multivalued treatments.
Computational psychiatry is a field aimed at developing formal models of information processing in the human brain, and how alterations in this processing can lead to clinical phenomena. Despite significant progress in the development of tasks and how to model them, computational psychiatry methodologies have yet to be incorporated into large-scale research projects or into clinical practice. In this viewpoint, we explore some of the barriers to incorporation of computational psychiatry tasks and models into wider mainstream research directions. These barriers include the time required for participants to complete tasks, test-retest reliability, limited ecological validity, as well as practical concerns, such as lack of computational expertise and the expense and large sample sizes traditionally required to validate tasks and models. We then discuss solutions, such as the redesigning of tasks with a view toward feasibility, and the integration of tasks into more ecologically valid and standardized game platforms that can be more easily disseminated. Finally, we provide an example of how one task, the conditioned hallucinations task, might be translated into such a game. It is our hope that interest in the creation of more accessible and feasible computational tasks will help computational methods make more positive impacts on research as well as clinical practice.
In practice, we can not only disable some events, but also enforce the occurrence of some events prior to the occurrence of other events by external control. In this paper, we combine these two control mechanisms to synthesize a more powerful supervisor. Here our control goal is to design an isolation supervisor which ensures in the closed-loop system, faults are isolatable in the sense that after a fault occurs, we can determine which type the fault belongs to by observing the output of the closed-loop system. The isolation supervisor starts to work when the occurrence of faults is detected. We then solve the isolation supervisor synthesis problem as follows. For a given discrete event system, we firstly construct a bipartite transition system which includes all feasible isolation supervisors. An isolation supervisor is feasible if it enforces only events that are physically possible. We then develop an algorithm to check whether the synthesis problem is solvable or not. The algorithm can also be used to find a valid isolation supervisor if the synthesis problem is solvable. The method of combining two control mechanisms can be used to synthesize more powerful supervisors for other supervisory control problems of discrete event systems as well.
This paper proves a new central limit theorem for a sample that exhibits two-way dependence and heterogeneity across clusters. Statistical inference for situations with both two-way dependence and cluster heterogeneity has thus far been an open issue. The existing theory for two-way clustering inference requires identical distributions across clusters (implied by the so-called separate exchangeability assumption). Yet no such homogeneity requirement is needed in the existing theory for one-way clustering. The new result therefore theoretically justifies the view that two-way clustering is a more robust version of one-way clustering, consistent with applied practice. In an application to linear regression, I show that a standard plug-in variance estimator is valid for inference.
Various saliency map methods have been proposed to interpret and explain predictions of deep learning models. Saliency maps allow us to interpret which parts of the input signals have a strong influence on the prediction results. However, since a saliency map is obtained by complex computations in deep learning models, it is often difficult to know how reliable the saliency map itself is. In this study, we propose a method to quantify the reliability of a salient region in the form of p-values. Our idea is to consider a salient region as a selected hypothesis by the trained deep learning model and employ the selective inference framework. The proposed method can provably control the probability of false positive detections of salient regions. We demonstrate the validity of the proposed method through numerical examples in synthetic and real datasets. Furthermore, we develop a Keras-based framework for conducting the proposed selective inference for a wide class of CNNs without additional implementation cost.
The recent spike in certified Artificial Intelligence (AI) tools for healthcare has renewed the debate around adoption of this technology. One thread of such debate concerns Explainable AI (XAI) and its promise to render AI devices more transparent and trustworthy. A few voices active in the medical AI space have expressed concerns on the reliability of Explainable AI techniques and especially feature attribution methods, questioning their use and inclusion in guidelines and standards. Despite valid concerns, we argue that existing criticism on the viability of post-hoc local explainability methods throws away the baby with the bathwater by generalizing a problem that is specific to image data. We begin by characterizing the problem as a lack of semantic match between explanations and human understanding. To understand when feature importance can be used reliably, we introduce a distinction between feature importance of low- and high-level features. We argue that for data types where low-level features come endowed with a clear semantics, such as tabular data like Electronic Health Records (EHRs), semantic match can be obtained, and thus feature attribution methods can still be employed in a meaningful and useful way. Finally, we sketch a procedure to test whether semantic match has been achieved.
Neighborhood gentrification plays a significant role in shaping the social and economic well-being of both individuals and communities at large. While some efforts have been made to detect gentrification in cities, existing approaches rely mainly on estimated measures from survey data, require substantial work of human labeling, and are limited in characterizing the neighborhood as a whole. We propose a novel approach to detecting neighborhood gentrification at a large-scale based on the physical appearance of neighborhoods by incorporating historical street-level visual data. We show the effectiveness of the proposed method by comparing results from our approach with gentrification measures from previous literature and case studies. Our approach has the potential to supplement existing indicators of gentrification and become a valid resource for urban researchers and policy makers.
The classical two-species non-linear Predator-Prey system, often used in population dynamics modeling, is expressed in terms of a single positive coupling parameter $\lambda$. Based on standard logarithmic transformations, we derive a novel $\lambda$-\textit{invariant} Hamiltonian resulting in two coupled first-order ODEs for ``hybrid-species'', \textit{albeit} with one being \textit{linear}; we thus derive a new exact, closed-form, single quadrature solution valid for any value of $\lambda$ and the system's energy. In the particular case $\lambda = 1$ the ODE system completely uncouples and a new, exact, energy-only dependent simple quadrature solution is derived. In the case $\lambda \neq 1$ an accurate practical approximation uncoupling the non-linear system is proposed and solutions are provided in terms of explicit quadratures together with high energy asymptotic solutions. A novel, exact, closed-form expression of the system's oscillation period valid for any value of $\lambda$ and orbital energy is also derived; two fundamental properties of the period are established; for $\lambda = 1$ the period is expressed in terms of a universal energy function and shown to be the shortest.
In this work, the Fourier-cosine series (COS) method has been combined with the Boundary Element Method (BEM) for a fast evaluation of barrier option prices. After a description of its use in the Black and Scholes (BS) model, the focus of the paper is on the application of the proposed methodology to the barrier option evaluation in the Heston model, where its contribution is fundamental to improve computational efficiency and to make BEM appealing among Finance practitioners as a valid alternative to Monte Carlo (MC) or other more traditional approaches. An error analysis is provided on the number of terms used in the Fourier-cosine series expansion, where the error bound estimation is based on the characteristic function of the log-asset price process.
In a diverse population, where many species are present, competitors can fight for surviving at individual and collective levels. In particular, species, which would beat each other individually, may form a specific alliance that ensures them stable coexistence against the invasion of an external species. Our principal goal is to identify those general features of a formation which determine its vitality. Therefore, we here study a traditional Lotka-Volterra model of eight-species where two four-species cycles can fight for space. Beside these formations, there are other solutions which may emerge when invasion rates are varied. The complete range of parameters is explored and we find that in most of the cases those alliances prevail which are formed by equally strong members. Interestingly, there are regions where the symmetry is broken and the system is dominated by a solution formed by seven species. Our work also highlights that serious finite-size effects may emerge which prevent observing the valid solution in a small system.
This paper proposes a novel testing procedure for selecting a sparse set of covariates that explains a large dimensional panel. Our selection method provides correct false detection control while having higher power than existing approaches. We develop the inferential theory for large panels with many covariates by combining post-selection inference with a novel multiple testing adjustment. Our data-driven hypotheses are conditional on the sparse covariate selection. We control for family-wise error rates for covariate discovery for large cross-sections. As an easy-to-use and practically relevant procedure, we propose Panel-PoSI, which combines the data-driven adjustment for panel multiple testing with valid post-selection p-values of a generalized LASSO, that allows us to incorporate priors. In an empirical study, we select a small number of asset pricing factors that explain a large cross-section of investment strategies. Our method dominates the benchmarks out-of-sample due to its better size and power.
Capturing feature information effectively is of great importance in vision tasks. With the development of convolutional neural networks (CNNs), concepts like residual connection and multiple scales promote continual performance gains on diverse deep learning vision tasks. However, the existing methods do not organically combined advantages of these valid ideas. In this paper, we propose a novel CNN architecture called GoogLe2Net, it consists of residual feature-reutilization inceptions (ResFRI) or split residual feature-reutilization inceptions (Split-ResFRI) which create transverse passages between adjacent groups of convolutional layers to enable features flow to latter processing branches and possess residual connections to better process information. Our GoogLe2Net is able to reutilize information captured by foregoing groups of convolutional layers and express multi-scale features at a fine-grained level, which improves performances in image classification. And the inception we proposed could be embedded into inception-like networks directly without any migration costs. Moreover, in experiments based on popular vision datasets, such as CIFAR10 (97.94%), CIFAR100 (85.91%) and Tiny Imagenet (70.54%), we obtain better results on image classification task compared with other modern models.