As predictive models -- e.g., from machine learning -- give likely outcomes, they may be used to reason on the effect of an intervention, a causal-inference task. The increasing complexity of health data has opened the door to a plethora of models, but also the Pandora box of model selection: which of these models yield the most valid causal estimates? Here we highlight that classic machine-learning model selection does not select the best outcome models for causal inference. Indeed, causal model selection should control both outcome errors for each individual, treated or not treated, whereas only one outcome is observed. Theoretically, simple risks used in machine learning do not control causal effects when treated and non-treated population differ too much. More elaborate risks build proxies of the causal error using ``nuisance'' re-weighting to compute it on the observed data. But does computing these nuisance adds noise to model selection? Drawing from an extensive empirical study, we outline a good causal model-selection procedure: using the so-called $R\text{-risk}$; using flexible estimators to compute the nuisance models on the train set; and splitting out 10\% of the data to compute risks.
Offline reinforcement learning is important in domains such as medicine, economics, and e-commerce where online experimentation is costly, dangerous or unethical, and where the true model is unknown. However, most methods assume all covariates used in the behavior policy's action decisions are observed. Though this assumption, sequential ignorability/unconfoundedness, likely does not hold in observational data, most of the data that accounts for selection into treatment may be observed, motivating sensitivity analysis. We study robust policy evaluation and policy optimization in the presence of sequentially-exogenous unobserved confounders under a sensitivity model. We propose and analyze orthogonalized robust fitted-Q-iteration that uses closed-form solutions of the robust Bellman operator to derive a loss minimization problem for the robust Q function, and adds a bias-correction to quantile estimation. Our algorithm enjoys the computational ease of fitted-Q-iteration and statistical improvements (reduced dependence on quantile estimation error) from orthogonalization. We provide sample complexity bounds, insights, and show effectiveness both in simulations and on real-world longitudinal healthcare data of treating sepsis. In particular, our model of sequential unobserved confounders yields an online Markov decision process, rather than partially observed Markov decision process: we illustrate how this can enable warm-starting optimistic reinforcement learning algorithms with valid robust bounds from observational data.
To date, the majority of positioning systems have been designed to operate within environments that have long-term stable macro-structure with potential small-scale dynamics. These assumptions allow the existing positioning systems to produce and utilize stable maps. However, in highly dynamic industrial settings these assumptions are no longer valid and the task of tracking people is more challenging due to the rapid large-scale changes in structure. In this paper we propose a novel positioning system for tracking people in highly dynamic industrial environments, such as construction sites. The proposed system leverages the existing CCTV camera infrastructure found in many industrial settings along with radio and inertial sensors within each worker's mobile phone to accurately track multiple people. This multi-target multi-sensor tracking framework also allows our system to use cross-modality training in order to deal with the environment dynamics. In particular, we show how our system uses cross-modality training in order to automatically keep track environmental changes (i.e. new walls) by utilizing occlusion maps. In addition, we show how these maps can be used in conjunction with social forces to accurately predict human motion and increase the tracking accuracy. We have conducted extensive real-world experiments in a construction site showing significant accuracy improvement via cross-modality training and the use of social forces.
The recently published paper by Gupta and Agrawal [1] exploited the sum-difference co-array (SDCA) to enhance the virtual aperture of sparse arrays. We argue that the key SDCA property established in [1] requires a critical necessary and sufficient condition that is valid for a very rare case only.
Sparse model identification enables nonlinear dynamical system discovery from data. However, the control of false discoveries for sparse model identification is challenging, especially in the low-data and high-noise limit. In this paper, we perform a theoretical study on ensemble sparse model discovery, which shows empirical success in terms of accuracy and robustness to noise. In particular, we analyse the bootstrapping-based sequential thresholding least-squares estimator. We show that this bootstrapping-based ensembling technique can perform a provably correct variable selection procedure with an exponential convergence rate of the error rate. In addition, we show that the ensemble sparse model discovery method can perform computationally efficient uncertainty estimation, compared to expensive Bayesian uncertainty quantification methods via MCMC. We demonstrate the convergence properties and connection to uncertainty quantification in various numerical studies on synthetic sparse linear regression and sparse model discovery. The experiments on sparse linear regression support that the bootstrapping-based sequential thresholding least-squares method has better performance for sparse variable selection compared to LASSO, thresholding least-squares, and bootstrapping-based LASSO. In the sparse model discovery experiment, we show that the bootstrapping-based sequential thresholding least-squares method can provide valid uncertainty quantification, converging to a delta measure centered around the true value with increased sample sizes. Finally, we highlight the improved robustness to hyperparameter selection under shifting noise and sparsity levels of the bootstrapping-based sequential thresholding least-squares method compared to other sparse regression methods.
A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample features) are inexpensive to access, but their group memberships (or labels) are costly. To address the problem, we devise the first \emph{active sequential two-sample testing framework} that not only sequentially but also \emph{actively queries}. Our test statistic is a likelihood ratio where one likelihood is found by maximization over all class priors, and the other is provided by a probabilistic classification model. The classification model is adaptively updated and used to predict where the (unlabelled) features have a high dependency on labels; labeling the ``high-dependency'' features leads to the increased power of the proposed testing framework. In theory, we provide the proof that our framework produces an \emph{anytime-valid} $p$-value. In addition, we characterize the proposed framework's gain in testing power by analyzing the mutual information between the feature and label variables in asymptotic and finite-sample scenarios. In practice, we introduce an instantiation of our framework and evaluate it using several experiments; the experiments on the synthetic, MNIST, and application-specific datasets demonstrate that the testing power of the instantiated active sequential test significantly increases while the Type I error is under control.
Dynamic treatment regimes or policies are a sequence of decision functions over multiple stages that are tailored to individual features. One important class of treatment policies in practice, namely multi-stage stationary treatment policies, prescribes treatment assignment probabilities using the same decision function across stages, where the decision is based on the same set of features consisting of time-evolving variables (e.g., routinely collected disease biomarkers). Although there has been extensive literature on constructing valid inference for the value function associated with dynamic treatment policies, little work has focused on the policies themselves, especially in the presence of high-dimensional feature variables. We aim to fill the gap in this work. Specifically, we first estimate the multi-stage stationary treatment policy using an augmented inverse probability weighted estimator for the value function to increase asymptotic efficiency, and further apply a penalty to select important feature variables. We then construct one-step improvements of the policy parameter estimators for valid inference. Theoretically, we show that the improved estimators are asymptotically normal, even if nuisance parameters are estimated at a slow convergence rate and the dimension of the feature variables increases with the sample size. Our numerical studies demonstrate that the proposed method estimates a sparse policy with a near-optimal value function and conducts valid inference for the policy parameters.
Assortment optimization has received active explorations in the past few decades due to its practical importance. Despite the extensive literature dealing with optimization algorithms and latent score estimation, uncertainty quantification for the optimal assortment still needs to be explored and is of great practical significance. Instead of estimating and recovering the complete optimal offer set, decision-makers may only be interested in testing whether a given property holds true for the optimal assortment, such as whether they should include several products of interest in the optimal set, or how many categories of products the optimal set should include. This paper proposes a novel inferential framework for testing such properties. We consider the widely adopted multinomial logit (MNL) model, where we assume that each customer will purchase an item within the offered products with a probability proportional to the underlying preference score associated with the product. We reduce inferring a general optimal assortment property to quantifying the uncertainty associated with the sign change point detection of the marginal revenue gaps. We show the asymptotic normality of the marginal revenue gap estimator, and construct a maximum statistic via the gap estimators to detect the sign change point. By approximating the distribution of the maximum statistic with multiplier bootstrap techniques, we propose a valid testing procedure. We also conduct numerical experiments to assess the performance of our method.
A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change is interpreted that this observation brings in extra information and, in learning theory, this corresponds to misclassification, or misprediction. In this paper, we lay the foundations of a new theory that allows one to keep control on the probability of change of compression (which maps into the statistical "risk" in learning applications). Under suitable conditions, the cardinality of the compressed set is shown to be a consistent estimator of the probability of change of compression (without any upper limit on the size of the compressed set); moreover, unprecedentedly tight finite-sample bounds to evaluate the probability of change of compression are obtained under a generally applicable condition of preference. All results are usable in a fully agnostic setup, i.e., without requiring any a priori knowledge on the probability distribution of the observations. Not only these results offer a valid support to develop trust in observation-driven methodologies, they also play a fundamental role in learning techniques as a tool for hyper-parameter tuning.
The present paper proposes a new treatment effects estimator that is valid when the number of time periods is small, and the parallel trends condition holds conditional on covariates and unobserved heterogeneity in the form of interactive fixed effects. The estimator also allow the control variables to be affected by treatment and it enables estimation of the resulting indirect effect on the outcome variable. The asymptotic properties of the estimator are established and their accuracy in small samples is investigated using Monte Carlo simulations. The empirical usefulness of the estimator is illustrated using as an example the effect of increased trade competition on firm markups in China.
Convolutional neural networks (CNN) have been successful in machine learning applications. Their success relies on their ability to consider space invariant local features. We consider the use of CNN to fit nuisance models in semiparametric estimation of the average causal effect of a treatment. In this setting, nuisance models are functions of pre-treatment covariates that need to be controlled for. In an application where we want to estimate the effect of early retirement on a health outcome, we propose to use CNN to control for time-structured covariates. Thus, CNN is used when fitting nuisance models explaining the treatment and the outcome. These fits are then combined into an augmented inverse probability weighting estimator yielding efficient and uniformly valid inference. Theoretically, we contribute by providing rates of convergence for CNN equipped with the rectified linear unit activation function and compare it to an existing result for feedforward neural networks. We also show when those rates guarantee uniformly valid inference. A Monte Carlo study is provided where the performance of the proposed estimator is evaluated and compared with other strategies. Finally, we give results on a study of the effect of early retirement on hospitalization using data covering the whole Swedish population.
Counterfactual explanations play an important role in detecting bias and improving the explainability of data-driven classification models. A counterfactual explanation (CE) is a minimal perturbed data point for which the decision of the model changes. Most of the existing methods can only provide one CE, which may not be achievable for the user. In this work we derive an iterative method to calculate robust CEs, i.e. CEs that remain valid even after the features are slightly perturbed. To this end, our method provides a whole region of CEs allowing the user to choose a suitable recourse to obtain a desired outcome. We use algorithmic ideas from robust optimization and prove convergence results for the most common machine learning methods including logistic regression, decision trees, random forests, and neural networks. Our experiments show that our method can efficiently generate globally optimal robust CEs for a variety of common data sets and classification models.
This work examines a social learning problem, where dispersed agents connected through a network topology interact locally to form their opinions (beliefs) as regards certain hypotheses of interest. These opinions evolve over time, since the agents collect observations from the environment, and update their current beliefs by accounting for: their past beliefs, the innovation contained in the new data, and the beliefs received from the neighbors. The distinguishing feature of the present work is that agents are constrained to share opinions regarding only a single hypothesis. We devise a novel learning strategy where each agent forms a valid belief by completing the partial beliefs received from its neighbors. This completion is performed by exploiting the knowledge accumulated in the past beliefs, thanks to a principled memory-aware rule inspired by a Bayesian criterion. The analysis allows us to characterize the role of memory in social learning under partial information sharing, revealing novel and nontrivial learning dynamics. Surprisingly, we establish that the standard classification rule based on selecting the maximum belief is not optimal under partial information sharing, while there exists a consistent threshold-based decision rule that allows each agent to classify correctly the hypothesis of interest. We also show that the proposed strategy outperforms previously considered schemes, highlighting that the introduction of memory in the social learning algorithm is critical to overcome the limitations arising from sharing partial information.
In the field of Automated Planning there is often the need for a set of planning problems from a particular domain, e.g., to be used as training data for Machine Learning or as benchmarks in planning competitions. In most cases, these problems are created either by hand or by a domain-specific generator, putting a burden on the human designers. In this paper we propose NeSIG, to the best of our knowledge the first domain-independent method for automatically generating planning problems that are valid, diverse and difficult to solve. We formulate problem generation as a Markov Decision Process and train two generative policies with Deep Reinforcement Learning to generate problems with the desired properties. We conduct experiments on three classical domains, comparing our approach against handcrafted, domain-specific instance generators and various ablations. Results show NeSIG is able to automatically generate valid and diverse problems of much greater difficulty (15.5 times more on geometric average) than domain-specific generators, while simultaneously reducing human effort when compared to them. Additionally, it can generalize to larger problems than those seen during training.
Fallacies are used as seemingly valid arguments to support a position and persuade the audience about its validity. Recognizing fallacies is an intrinsically difficult task both for humans and machines. Moreover, a big challenge for computational models lies in the fact that fallacies are formulated differently across the datasets with differences in the input format (e.g., question-answer pair, sentence with fallacy fragment), genre (e.g., social media, dialogue, news), as well as types and number of fallacies (from 5 to 18 types per dataset). To move towards solving the fallacy recognition task, we approach these differences across datasets as multiple tasks and show how instruction-based prompting in a multitask setup based on the T5 model improves the results against approaches built for a specific dataset such as T5, BERT or GPT-3. We show the ability of this multitask prompting approach to recognize 28 unique fallacies across domains and genres and study the effect of model size and prompt choice by analyzing the per-class (i.e., fallacy type) results. Finally, we analyze the effect of annotation quality on model performance, and the feasibility of complementing this approach with external knowledge.
A Deep Neural Network (DNN) is a composite function of vector-valued functions, and in order to train a DNN, it is necessary to calculate the gradient of the loss function with respect to all parameters. This calculation can be a non-trivial task because the loss function of a DNN is a composition of several nonlinear functions, each with numerous parameters. The Backpropagation (BP) algorithm leverages the composite structure of the DNN to efficiently compute the gradient. As a result, the number of layers in the network does not significantly impact the complexity of the calculation. The objective of this paper is to express the gradient of the loss function in terms of a matrix multiplication using the Jacobian operator. This can be achieved by considering the total derivative of each layer with respect to its parameters and expressing it as a Jacobian matrix. The gradient can then be represented as the matrix product of these Jacobian matrices. This approach is valid because the chain rule can be applied to a composition of vector-valued functions, and the use of Jacobian matrices allows for the incorporation of multiple inputs and outputs. By providing concise mathematical justifications, the results can be made understandable and useful to a broad audience from various disciplines.
Both the Bayes factor and the relative belief ratio satisfy the principle of evidence and so can be seen to be valid measures of statistical evidence. Certainly Bayes factors are regularly employed. The question then is: which of these measures of evidence is more appropriate? It is argued here that there are questions concerning the validity of a current commonly used definition of the Bayes factor based on a mixture prior and, when all is considered, the relative belief ratio has better properties as a measure of evidence. It is further shown that, when a natural restriction on the mixture prior is imposed, the Bayes factor equals the relative belief ratio obtained without using the mixture prior. Even with this restriction, this still leaves open the question of how the strength of evidence is to be measured. It is argued here that the current practice of using the size of the Bayes factor to measure strength is not correct and a solution to this issue is presented. Several general criticisms of these measures of evidence are also discussed and addressed.
The main objective of this work is to test whether some stochastic models typically used in financial markets could be applied to the COVID-19 pandemic. To this end we have implemented the ARIMAX and Cox-Ingersoll-Ross (CIR) models originally designed for interest rate pricing but transformed by us into a forecasting tool. For the latter, which we denoted CIR*, both the Euler-Maruyama method and the Milstein method were used. Forecasts obtained with the maximum likelihood method have been validated with 95\% confidence intervals and with statistical measures of goodness of fit, such as the root mean square error (RMSE). We demonstrate that the accuracy of the obtained results is consistent with the observations and sufficiently accurate to the point that the proposed CIR* framework could be considered a valid alternative to the classical ARIMAX for modelling pandemics.
Closed-loop negative feedback mechanism is extensively utilized in automatic control systems and brings about extraordinary dynamic and static performance. In order to further improve the reconstruction capability of current methods of compressed image super-resolution, a circular Swin2SR (CSwin2SR) approach is proposed. The CSwin2SR contains a serial Swin2SR for initial super-resolution reestablishment and circular Swin2SR for enhanced super-resolution reestablishment. Simulated experimental results show that the proposed CSwin2SR dramatically outperforms the classical Swin2SR in the capacity of super-resolution recovery. On DIV2K test and valid datasets, the average increment of PSNR is greater than 0.18 dB and the related average increment of SSIM is greater than 0.01.
Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known upper bound on the $p$-th central moment ($p$ > 1), but allowing for (at most) $\epsilon$ fraction of arbitrary distribution corruption, as in Huber's contamination model. We do this by designing new robust exponential supermartingales, and show that the resulting confidence sequences attain the optimal width achieved in the nonsequential setting. Perhaps surprisingly, the constant margin between our sequential result and the lower bound is smaller than even fixed-time robust confidence intervals based on the trimmed mean, for example. Since confidence sequences are a common tool used within A/B/n testing and bandits, these results open the door to sequential experimentation that is robust to outliers and adversarial corruptions.