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This work considers Gaussian process interpolation with a periodized version of the Mat{\'e}rn covariance function introduced by Stein (22, Section 6.7). Convergence rates are studied for the joint maximum likelihood estimation of the regularity and the amplitude parameters when the data is sampled according to the model. The mean integrated squared error is also analyzed with fixed and estimated parameters, showing that maximum likelihood estimation yields asymptotically the same error as if the ground truth was known. Finally, the case where the observed function is a fixed deterministic element of a Sobolev space of continuous functions is also considered, suggesting that bounding assumptions on some parameters can lead to different estimates.

The Fisher information matrix (FIM) is a key quantity in statistics as it is required for example for evaluating asymptotic precisions of parameter estimates, for computing test statistics or asymptotic distributions in statistical testing, for evaluating post model selection inference results or optimality criteria in experimental designs. However its exact computation is often not trivial. In particular in many latent variable models, it is intricated due to the presence of unobserved variables. Therefore the observed FIM is usually considered in this context to estimate the FIM. Several methods have been proposed to approximate the observed FIM when it can not be evaluated analytically. Among the most frequently used approaches are Monte-Carlo methods or iterative algorithms derived from the missing information principle. All these methods require to compute second derivatives of the complete data log-likelihood which leads to some disadvantages from a computational point of view. In this paper, we present a new approach to estimate the FIM in latent variable model. The advantage of our method is that only the first derivatives of the log-likelihood is needed, contrary to other approaches based on the observed FIM. Indeed we consider the empirical estimate of the covariance matrix of the score. We prove that this estimate of the Fisher information matrix is unbiased, consistent and asymptotically Gaussian. Moreover we highlight that none of both estimates is better than the other in terms of asymptotic covariance matrix. When the proposed estimate can not be directly analytically evaluated, we present a stochastic approximation estimation algorithm to compute it. This algorithm provides this estimate of the FIM as a by-product of the parameter estimates. We emphasize that the proposed algorithm only requires to compute the first derivatives of the complete data log-likelihood with respect to the parameters. We prove that the estimation algorithm is consistent and asymptotically Gaussian when the number of iterations goes to infinity. We evaluate the finite sample size properties of the proposed estimate and of the observed FIM through simulation studies in linear mixed effects models and mixture models. We also investigate the convergence properties of the estimation algorithm in non linear mixed effects models. We compare the performances of the proposed algorithm to those of other existing methods.

Mobile applications are widely used for online services sharing a large amount of personal data online. One-time authentication techniques such as passwords and physiological biometrics (e.g., fingerprint, face, and iris) have their own advantages but also disadvantages since they can be stolen or emulated, and do not prevent access to the underlying device, once it is unlocked. To address these challenges, complementary authentication systems based on behavioural biometrics have emerged. The goal is to continuously profile users based on their interaction with the mobile device. However, existing behavioural authentication schemes are not (i) user-agnostic meaning that they cannot dynamically handle changes in the user-base without model re-training, or (ii) do not scale well to authenticate millions of users. In this paper, we present AuthentiSense, a user-agnostic, scalable, and efficient behavioural biometrics authentication system that enables continuous authentication and utilizes only motion patterns (i.e., accelerometer, gyroscope and magnetometer data) while users interact with mobile apps. Our approach requires neither manually engineered features nor a significant amount of data for model training. We leverage a few-shot learning technique, called Siamese network, to authenticate users at a large scale. We perform a systematic measurement study and report the impact of the parameters such as interaction time needed for authentication and n-shot verification (comparison with enrollment samples) at the recognition stage. Remarkably, AuthentiSense achieves high accuracy of up to 97% in terms of F1-score even when evaluated in a few-shot fashion that requires only a few behaviour samples per user (3 shots). Our approach accurately authenticates users only after 1 second of user interaction. For AuthentiSense, we report a FAR and FRR of 0.023 and 0.057, respectively.

In recent years fairness in machine learning (ML) has emerged as a highly active area of research and development. Most define fairness in simple terms, where fairness means reducing gaps in performance or outcomes between demographic groups while preserving as much of the accuracy of the original system as possible. This oversimplification of equality through fairness measures is troubling. Many current fairness measures suffer from both fairness and performance degradation, or "levelling down," where fairness is achieved by making every group worse off, or by bringing better performing groups down to the level of the worst off. When fairness can only be achieved by making everyone worse off in material or relational terms through injuries of stigma, loss of solidarity, unequal concern, and missed opportunities for substantive equality, something would appear to have gone wrong in translating the vague concept of 'fairness' into practice. This paper examines the causes and prevalence of levelling down across fairML, and explore possible justifications and criticisms based on philosophical and legal theories of equality and distributive justice, as well as equality law jurisprudence. We find that fairML does not currently engage in the type of measurement, reporting, or analysis necessary to justify levelling down in practice. We propose a first step towards substantive equality in fairML: "levelling up" systems by design through enforcement of minimum acceptable harm thresholds, or "minimum rate constraints," as fairness constraints. We likewise propose an alternative harms-based framework to counter the oversimplified egalitarian framing currently dominant in the field and push future discussion more towards substantive equality opportunities and away from strict egalitarianism by default. N.B. Shortened abstract, see paper for full abstract.

An assisted living facility (ALF) is a place where someone can live, have access to social supports such as transportation, and receive assistance with the activities of daily living such as toileting and dressing. Despite the important role of ALFs, they are not required to be certified with Medicare and there is no public national database of these facilities. We present the first public dataset of ALFs in the United States, covering all 50 states and DC with 44,638 facilities and over 1.2 million beds. This dataset can help provide answers to existing public health questions as well as help those in need find a facility. The dataset was validated by replicating the results of a nationwide study of ALFs that uses closed data [4], where the prevalence of ALFs is assessed with respect to county-level socioeconomic variables related to health disparity such as race, disability, and income. To showcase the value of this dataset, we also propose a novel metric to assess access to community-based care. We calculate the average distance an individual in need must travel in order to reach an ALF. The dataset and all relevant code are available at github.com/antonstengel/assisted-living-data.

Value decomposition methods have gradually become popular in the cooperative multi-agent reinforcement learning field. However, almost all value decomposition methods follow the Individual Global Max (IGM) principle or its variants, which restricts the range of issues that value decomposition methods can resolve. Inspired by the notion of dual self-awareness in psychology, we propose a dual self-awareness value decomposition framework that entirely rejects the IGM premise. Each agent consists of an ego policy that carries out actions and an alter ego value function that takes part in credit assignment. The value function factorization can ignore the IGM assumption by using an explicit search procedure. We also suggest a novel anti-ego exploration mechanism to avoid the algorithm becoming stuck in a local optimum. As the first fully IGM-free value decomposition method, our proposed framework achieves desirable performance in various cooperative tasks.

Missing data is common in applied data science, particularly for tabular data sets found in healthcare, social sciences, and natural sciences. Most supervised learning methods only work on complete data, thus requiring preprocessing such as missing value imputation to work on incomplete data sets. However, imputation alone does not encode useful information about the missing values themselves. For data sets with informative missing patterns, the Missing Indicator Method (MIM), which adds indicator variables to indicate the missing pattern, can be used in conjunction with imputation to improve model performance. While commonly used in data science, MIM is surprisingly understudied from an empirical and especially theoretical perspective. In this paper, we show empirically and theoretically that MIM improves performance for informative missing values, and we prove that MIM does not hurt linear models asymptotically for uninformative missing values. Additionally, we find that for high-dimensional data sets with many uninformative indicators, MIM can induce model overfitting and thus test performance. To address this issue, we introduce Selective MIM (SMIM), a novel MIM extension that adds missing indicators only for features that have informative missing patterns. We show empirically that SMIM performs at least as well as MIM in general, and improves MIM for high-dimensional data. Lastly, to demonstrate the utility of MIM on real-world data science tasks, we demonstrate the effectiveness of MIM and SMIM on clinical tasks generated from the MIMIC-III database of electronic health records.

Ensuring fairness in machine learning algorithms is a challenging and essential task. We consider the problem of clustering a set of points while satisfying fairness constraints. While there have been several attempts to capture group fairness in the $k$-clustering problem, fairness at an individual level is relatively less explored. We introduce a new notion of individual fairness in $k$-clustering based on features not necessarily used for clustering. We show that this problem is NP-hard and does not admit a constant factor approximation. Therefore, we design a randomized algorithm that guarantees approximation both in terms of minimizing the clustering distance objective and individual fairness under natural restrictions on the distance metric and fairness constraints. Finally, our experimental results against six competing baselines validate that our algorithm produces individually fairer clusters than the fairest baseline by 12.5% on average while also being less costly in terms of the clustering objective than the best baseline by 34.5% on average.

Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving the way for significant changes in computational engineering applications. Here, we investigate the use of DeepONets to infer flow fields around unseen airfoils with the aim of shape optimization, an important design problem in aerodynamics that typically taxes computational resources heavily. We present results which display little to no degradation in prediction accuracy, while reducing the online optimization cost by orders of magnitude. We consider NACA airfoils as a test case for our proposed approach, as their shape can be easily defined by the four-digit parametrization. We successfully optimize the constrained NACA four-digit problem with respect to maximizing the lift-to-drag ratio and validate all results by comparing them to a high-order CFD solver. We find that DeepONets have low generalization error, making them ideal for generating solutions of unseen shapes. Specifically, pressure, density, and velocity fields are accurately inferred at a fraction of a second, hence enabling the use of general objective functions beyond the maximization of the lift-to-drag ratio considered in the current work.

Click-through rate (CTR) prediction plays a critical role in recommender systems and online advertising. The data used in these applications are multi-field categorical data, where each feature belongs to one field. Field information is proved to be important and there are several works considering fields in their models. In this paper, we proposed a novel approach to model the field information effectively and efficiently. The proposed approach is a direct improvement of FwFM, and is named as Field-matrixed Factorization Machines (FmFM, or $FM^2$). We also proposed a new explanation of FM and FwFM within the FmFM framework, and compared it with the FFM. Besides pruning the cross terms, our model supports field-specific variable dimensions of embedding vectors, which acts as soft pruning. We also proposed an efficient way to minimize the dimension while keeping the model performance. The FmFM model can also be optimized further by caching the intermediate vectors, and it only takes thousands of floating-point operations (FLOPs) to make a prediction. Our experiment results show that it can out-perform the FFM, which is more complex. The FmFM model's performance is also comparable to DNN models which require much more FLOPs in runtime.