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In the pursuit of enhancing the efficacy and flexibility of interpretable, data-driven classification models, this work introduces a novel incorporation of user-defined preferences with Abstract Argumentation and Case-Based Reasoning (CBR). Specifically, we introduce Preference-Based Abstract Argumentation for Case-Based Reasoning (which we call AA-CBR-P), allowing users to define multiple approaches to compare cases with an ordering that specifies their preference over these comparison approaches. We prove that the model inherently follows these preferences when making predictions and show that previous abstract argumentation for case-based reasoning approaches are insufficient at expressing preferences over constituents of an argument. We then demonstrate how this can be applied to a real-world medical dataset sourced from a clinical trial evaluating differing assessment methods of patients with a primary brain tumour. We show empirically that our approach outperforms other interpretable machine learning models on this dataset., Comment: Accepted for KR2024. Includes Appendix

This paper studies the relationship between quadratic Hodge classes on moduli spaces of pseudostable and stable curves given by the contraction morphism $\mathcal{T}.$ While Mumford relations do not hold in the pseudostable case, we show that one can express the (pullback via $\mathcal{T}$ of the) Chern classes of $\mathbb{E}\oplus \mathbb{E}^\vee$ solely in terms of descendants and strata classes. We organize the combinatorial structure of the pullback of products of two pseudostable $\lambda$ classes and obtain an explicit comparison of arbitrary pseudostable and stable quadratic Hodge integrals.

We prove that if a certain entry in the map of the Hadamard-Perron theorem is $T$-periodic in one of the variables, then the stable manifold guaranteed by the Hadamard-Perron theorem is a graph of a $T$-periodic function. As an application, we extend the classical Levinson's result about the occurrence of an attracting closed invariant curve near a stable cycle of a system of autonomous equations under periodic perturbations to hybrid differential equations.

Feature attribution methods are widely used to explain neural models by determining the influence of individual input features on the models' outputs. We propose a novel feature attribution method, CAFE (Conflict-Aware Feature-wise Explanations), that addresses three limitations of the existing methods: their disregard for the impact of conflicting features, their lack of consideration for the influence of bias terms, and an overly high sensitivity to local variations in the underpinning activation functions. Unlike other methods, CAFE provides safeguards against overestimating the effects of neuron inputs and separately traces positive and negative influences of input features and biases, resulting in enhanced robustness and increased ability to surface feature conflicts. We show experimentally that CAFE is better able to identify conflicting features on synthetic tabular data and exhibits the best overall fidelity on several real-world tabular datasets, while being highly computationally efficient.

Poor diet quality is a key modifiable risk factor for hypertension and disproportionately impacts low-income women. \sw{Analyzing diet-driven hypertensive outcomes in this demographic is challenging due to the complexity of dietary data and selection bias when the data come from surveys, a main data source for understanding diet-disease relationships in understudied populations. Supervised Bayesian model-based clustering methods summarize dietary data into latent patterns that holistically capture relationships among foods and a known health outcome but do not sufficiently account for complex survey design. This leads to biased estimation and inference and lack of generalizability of the patterns}. To address this, we propose a supervised weighted overfitted latent class analysis (SWOLCA) based on a Bayesian pseudo-likelihood approach that integrates sampling weights into an exposure-outcome model for discrete data. Our model adjusts for stratification, clustering, and informative sampling, and handles modifying effects via interaction terms within a Markov chain Monte Carlo Gibbs sampling algorithm. Simulation studies confirm that the SWOLCA model exhibits good performance in terms of bias, precision, and coverage. Using data from the National Health and Nutrition Examination Survey (2015-2018), we demonstrate the utility of our model by characterizing dietary patterns associated with hypertensive outcomes among low-income women in the United States., Comment: 16 pages, 8 tables, 7 figures

Neural networks (NNs) can learn to rely on spurious signals in the training data, leading to poor generalisation. Recent methods tackle this problem by training NNs with additional ground-truth annotations of such signals. These methods may, however, let spurious signals re-emerge in deep convolutional NNs (CNNs). We propose Targeted Activation Penalty (TAP), a new method tackling the same problem by penalising activations to control the re-emergence of spurious signals in deep CNNs, while also lowering training times and memory usage. In addition, ground-truth annotations can be expensive to obtain. We show that TAP still works well with annotations generated by pre-trained models as effective substitutes of ground-truth annotations. We demonstrate the power of TAP against two state-of-the-art baselines on the MNIST benchmark and on two clinical image datasets, using four different CNN architectures., Comment: 24 pages including appendix; extended version of a paper accepted to AAAI-2024 under the same title

By studying laminations of the unit disk, we can gain insight into the structure of Julia sets of polynomials and their dynamics in the complex plane. The polynomials of a given degree, $d$, have a parameter space. The hyperbolic components of such parameter spaces are in correspondence to rotational polygons, or classes of "rotational sets", which we study in this paper. By studying the count of such rotational sets, and therefore the underlying structure behind these rotational sets and polygons, we can gain insight into the interrelationship among hyperbolic components of the parameter space of these polynomials. These rotational sets are created by uniting rotational orbits, as we define in this paper. The number of such sets for a given degree $d$, rotation number $\frac pq$, and cardinality $k$ can be determined by analyzing the potential placements of pre-images of zero on the unit circle with respect to the rotational set under the $d$-tupling map. We obtain a closed-form formula for the count. Though this count is already known based upon some sophisticated results, our count is based upon elementary geometric and combinatorial principles, and provides an intuitive explanation., Comment: 12 pages, 5 figures

We present csSampling, an R package for estimation of Bayesian models for data collected from complex survey samples. csSampling combines functionality from the probabilistic programming language Stan (via the rstan and brms R packages) and the handling of complex survey data from the survey R package. Under this approach, the user creates a survey-weighted model in brms or provides a custom weighted model via rstan. Survey design information is provided via the svydesign function of the survey package. The cs_sampling function of csSampling estimates the weighted stan model and provides an asymptotic covariance correction for model mis-specification due to using survey sampling weights as plug-in values in the likelihood. This is often known as a ``design effect'' which is the ratio between the variance from a complex survey sample and a simple random sample of the same size. The resulting adjusted posterior draws can then be used for the usual Bayesian inference while also achieving frequentist properties of asymptotic consistency and correct uncertainty (e.g. coverage)., Comment: 22 pages, 5 figures

Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective sample size. Estimation of a population quantity derived from a convenience sample will typically result in bias since the distribution of variables of interest in the convenience sample is different from the population distribution. A recent set of approaches estimates inclusion probabilities for convenience sample units by specifying reference sample-weighted pseudo likelihoods. This paper introduces a novel approach that derives the propensity score for the observed sample as a function of inclusion probabilities for the reference and convenience samples as our main result. Our approach allows specification of a likelihood directly for the observed sample as opposed to the approximate or pseudo likelihood. We construct a Bayesian hierarchical formulation that simultaneously estimates sample propensity scores and the convenience sample inclusion probabilities. We use a Monte Carlo simulation study to compare our likelihood based results with the pseudo likelihood based approaches considered in the literature., Comment: 37 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:2204.02271

Recent research has shown the potential for neural networks to improve upon classical survival models such as the Cox model, which is widely used in clinical practice. Neural networks, however, typically rely on data that are centrally available, whereas healthcare data are frequently held in secure silos. We present a federated Cox model that accommodates this data setting and also relaxes the proportional hazards assumption, allowing time-varying covariate effects. In this latter respect, our model does not require explicit specification of the time-varying effects, reducing upfront organisational costs compared to previous works. We experiment with publicly available clinical datasets and demonstrate that the federated model is able to perform as well as a standard model., Comment: Accepted for publication in Multimodal AI in Healthcare: A Paradigm Shift in Health Intelligence as part of the book series Studies in Computational Intelligence by Springer

We perform spectral energy distribution (SED) fitting to 711 luminous X-ray AGN at 0.7 < z < 4.5 using 10-bands of optical and infra-red photometric data for objects within XMM-SERVS. This fitting provided 510 reliable (reduced $\chi ^2 < 3$) inferences on AGN and host galaxy properties. The AGN optical (3000\r{A}) luminosity inferred from SED-fitting is found to correlate with the measured X-ray (2-10 keV) luminosity, in good agreement with previous work. Using X-ray hardness as a proxy for AGN obscuration, we also study the differences in the host galaxy properties of obscured and unobscured AGN. Both populations have consistent stellar masses (log$_{10}(M_*/M_{\odot})$ = 10.88 $\pm0.09M_\odot$ and log$_{10}(M_*/M_{\odot})$ = 10.8 $\pm0.1M_\odot$ for unobscured and obscured AGN respectively). We also find evidence for varying AGN emission line properties from a standard AGN template in 18.8% of the sample with a reduced $\chi^2 < 3$ where the inclusion of an additional emission line strength free parameter was found to improve the quality of the fit. Comparison of these fits to SDSS spectra showed that emission line properties inferred from broadband photometry were consistent with the results from spectroscopy for 91% of objects. We find that the presence of weaker, more blueshifted emission lines as inferred from the SED fits are associated with more negative values of $\alpha_{ox}$. While the correlation between the hardness of the ionising SED and the emission line properties has been known for some time, we are able to derive this correlation purely from broadband photometry., Comment: 13 pages, 8 figures. Accepted for publication by MNRAS

This paper introduces a new method that embeds any Bayesian model used to generate synthetic data and converts it into a differentially private (DP) mechanism. We propose an alteration of the model synthesizer to utilize a censored likelihood that induces upper and lower bounds of [$\exp(-\epsilon / 2), \exp(\epsilon / 2)$], where $\epsilon$ denotes the level of the DP guarantee. This censoring mechanism equipped with an $\epsilon-$DP guarantee will induce distortion into the joint parameter posterior distribution by flattening or shifting the distribution towards a weakly informative prior. To minimize the distortion in the posterior distribution induced by likelihood censoring, we embed a vector-weighted pseudo posterior mechanism within the censoring mechanism. The pseudo posterior is formulated by selectively downweighting each likelihood contribution proportionally to its disclosure risk. On its own, the pseudo posterior mechanism produces a weaker asymptotic differential privacy (aDP) guarantee. After embedding in the censoring mechanism, the DP guarantee becomes strict such that it does not rely on asymptotics. We demonstrate that the pseudo posterior mechanism creates synthetic data with the highest utility at the price of a weaker, aDP guarantee, while embedding the pseudo posterior mechanism in the proposed censoring mechanism produces synthetic data with a stronger, non-asymptotic DP guarantee at the cost of slightly reduced utility. The perturbed histogram mechanism is included for comparison.

Although machine learning (ML) has shown promise in numerous domains, there are concerns about generalizability to out-of-sample data. This is currently addressed by centrally sharing ample, and importantly diverse, data from multiple sites. However, such centralization is challenging to scale (or even not feasible) due to various limitations. Federated ML (FL) provides an alternative to train accurate and generalizable ML models, by only sharing numerical model updates. Here we present findings from the largest FL study to-date, involving data from 71 healthcare institutions across 6 continents, to generate an automatic tumor boundary detector for the rare disease of glioblastoma, utilizing the largest dataset of such patients ever used in the literature (25,256 MRI scans from 6,314 patients). We demonstrate a 33% improvement over a publicly trained model to delineate the surgically targetable tumor, and 23% improvement over the tumor's entire extent. We anticipate our study to: 1) enable more studies in healthcare informed by large and diverse data, ensuring meaningful results for rare diseases and underrepresented populations, 2) facilitate further quantitative analyses for glioblastoma via performance optimization of our consensus model for eventual public release, and 3) demonstrate the effectiveness of FL at such scale and task complexity as a paradigm shift for multi-site collaborations, alleviating the need for data sharing., Comment: federated learning, deep learning, convolutional neural network, segmentation, brain tumor, glioma, glioblastoma, FeTS, BraTS

We propose two synthetic microdata approaches to generate private tabular survey data products for public release. We adapt a pseudo posterior mechanism that downweights by-record likelihood contributions with weights $\in [0,1]$ based on their identification disclosure risks to producing tabular products for survey data. Our method applied to an observed survey database achieves an asymptotic global probabilistic differential privacy guarantee. Our two approaches synthesize the observed sample distribution of the outcome and survey weights, jointly, such that both quantities together possess a privacy guarantee. The privacy-protected outcome and survey weights are used to construct tabular cell estimates (where the cell inclusion indicators are treated as known and public) and associated standard errors to correct for survey sampling bias. Through a real data application to the Survey of Doctorate Recipients public use file and simulation studies motivated by the application, we demonstrate that our two microdata synthesis approaches to construct tabular products provide superior utility preservation as compared to the additive-noise approach of the Laplace Mechanism. Moreover, our approaches allow the release of microdata to the public, enabling additional analyses at no extra privacy cost.

We address practical implementation of a risk-weighted pseudo posterior synthesizer for microdata dissemination with a new re-weighting strategy that maximizes utility of released synthetic data under at any level of formal privacy guarantee. Our re-weighting strategy applies to any vector-weighted pseudo posterior mechanism under which a vector of observation-indexed weights are used to downweight likelihood contributions for high disclosure risk records. We demonstrate our method on two different vector-weighted schemes that target high-risk records. Our new method for constructing record-indexed downeighting maximizes the data utility under any privacy budget for the vector-weighted synthesizers by adjusting the by-record weights, such that their individual Lipschitz bounds approach the bound for the entire database. Our method achieves an $(\epsilon = 2 \Delta_{\boldsymbol{\alpha}})-$asymptotic differential privacy (aDP) guarantee, globally, over the space of databases. We illustrate our methods using simulated highly skewed count data and compare the results to a scalar-weighted synthesizer under the Exponential Mechanism (EM). We also apply our methods to a sample of the Survey of Doctorate Recipients and demonstrate the practicality of our methods.

We devise survey-weighted pseudo posterior distribution estimators under two-stage informative sampling of both primary clusters and secondary nested units for a one-way analysis of variance (ANOVA) population generating model as a simple canonical case where population model random effects are defined to be coincident with the primary clusters, for example student performance based on a survey of schools and students such as the 2000 OECD Programme for International Student Assessment (PISA). We consider estimation on an observed informative sample under both an augmented pseudo likelihood that co-samples the random effects, as well as an integrated likelihood that marginalizes out the random effects from the survey-weighted augmented pseudo likelihood. This paper includes a theoretical exposition that enumerates easily verified conditions for which estimation under the augmented pseudo posterior is guaranteed to be consistent at the true generating parameters. We reveal in simulation that both approaches produce asymptotically unbiased estimation of the generating hyperparameters for the random effects when a key condition on the sum of within cluster weighted residuals is met. We present a comparison with two frequentist alternatives, an expectation-maximization approach and a composite likelihood method that requires pairwise sampling weights., Comment: 45 pages, 12 figures