Papers

We prove an all-allocation global target-risk theorem for independent Gaussian sources that share a scalar nuisance and an unknown contact coordinate. For a fixed immersed nuisance curve with finitely many multiple fibres and pairwise nonparallel branch tangents, squared target risk is comparable to a primary estimation floor plus a target-gap-weighted Gaussian discrimination profile. Independent localization, finite branch selection and target-class refitting give an estimator attaining this comparison across every nonnegative integer allocation. A full-box specialization has positive-definite primary Fisher information everywhere and globally identifies its target, yet models with identical derivatives of every order along a critical hypersurface have different polynomial risk exponents. We construct a finite certified estimator and quantify the numerical accuracy needed to preserve rare branch decisions and acquisition windows. A polynomial tangency family both demonstrates the geometric boundary and quantifies its repair: known auxiliary gain, source contact order and target vanishing order determine a risk law uniform through zero gain. For a shared spherical direction, a separately proved composite-testing result transfers through an unknown contact coordinate using only counted observations. These theorems distinguish the resources needed for local estimation, discrimination between parameter regions and nuisance alignment, and yield acquisition thresholds under explicit scalar-observation costs.

This paper proposes and studies a likelihood-ratio test of the null hypothesis that weak stochastic transitivity (WST) does not hold. This is the reverse of the formulation commonly used in the literature, where WST is set as the null hypothesis. We show that, even when the number of items grows with the number of comparisons per pair, the uniform size converges to the nominal level, with the critical value determined by a chi-bar-square distribution. We further establish that the Type II error converges uniformly to zero under a sufficient signal-strength condition. Simulation studies demonstrate good finite-sample Type I error control and show that power increases with the sample size and signal strength.

The optimal transport (OT) map provides a geometric transformation for aligning probability distributions and has become a useful tool in machine learning. However, existing estimators of the OT map still exhibit a gap between sharp statistical guarantees and practical parametric estimation based on stable training objectives. Theoretical estimators achieve minimax optimal convergence rates, but they are typically nonparametric and can incur demanding implementation design or inference costs. Practical estimators are parametric and scalable, but their statistical guarantees remain underexplored, and their min-max, adversarial-like training objectives can be sensitive to optimization algorithms. We propose BROT (Barycentric Regression for OT), a simple two-step method that first computes the unregularized OT plan and then fits a deep neural network (DNN) to the induced barycentric targets by least-squares regression. Under standard regularity conditions, we prove that the DNN estimator of BROT attains the minimax convergence rate, when the ground-truth OT map is Lipschitz. Numerical studies on synthetic datasets and an image dataset show that BROT provides accurate map estimates, strong target distribution matching, and competitive transport costs, compared to existing estimation methods. Experiments on two downstream tasks, single-cell perturbation prediction and unsupervised domain adaptation, further suggest that the accurate estimation of BROT can translate into stronger task performance.

Rank-based tests need no distributional assumptions to be valid, but the sample size they require does depend on the shapes of the two outcome distributions, which are unknown at the design stage. Standard practice substitutes a variance calibrated under the null. We ask how wrong that substitution can be. Writing $\Pi$ for the ratio of the true asymptotic variance of the estimated relative effect to the substituted one, we prove that under balanced allocation $\Pi \le 16\theta(1-\theta)/\{2+\theta(1-\theta)\} \le 16/9$ for all ordinal distributions in any number of categories: within the first-order asymptotic calculation the required sample size can exceed the calculated one by at most $77.8\%$, and an explicit two-point family attains the bound at every effect size. The effect-specific envelope, not the constant, is the operative quantity for a design: the ceiling falls to $1.63$ at $\theta=0.65$ and $1.37$ at $\theta=0.75$, so a trial powered for a larger effect is correspondingly less exposed. The proof is elementary. In five extracted trial comparisons and 4,711 generated alternatives the realized cost stays within a few percent, because the extremal configuration is one that shift-type treatment mechanisms do not produce. These facts are complementary, and fix how the bound should be used: it is a design sensitivity certificate, not an inflation factor. A protocol can report the conventional sample size alongside the largest requirement consistent with any ordinal configuration.

Partial missingness is common in high-dimensional data, but most existing change-point procedures are developed for fully observed sequences. We introduce gMiss, a graph-based framework for testing and localizing a change in the observed-data distribution of a partially observed high-dimensional sequence. The method treats the observed values together with the missingness indicators as the object of inference, so the target alternative is a change in the induced observed data law. It is designed for general distributional changes and requires neither sparsity nor Gaussianity. When the augmented observations are independent, the full permutation test controls type I error in finite samples. The procedure combines graph scans based on elementwise imputation and distance imputation. The two scans capture complementary graph patterns. Simulation results indicate that gMiss maintains accurate null calibration across the MCAR and MAR designs considered, remains competitive under Gaussian location alternatives, and exhibits strong power and localization performance in many non-Gaussian location and scale settings. We further illustrate the practical utility of the method through an application to genomic copy-number data, where gMiss identifies additional candidate boundaries that are visually plausible in the raw heatmap.

We construct tie-symmetrised extensions $\widetilde D$ and $\widetilde R$ of the unnormalised Hoeffding and Blum–Kiefer–Rosenblatt functionals $D$ and $R$ and prove, for every real-valued bivariate law, the exact nonnegative decomposition $ \tau^{*}(X,Y)=12\widetilde D(X,Y)+24\widetilde R(X,Y), \qquad \widetilde D,\widetilde R\geq0, \qquad \widetilde R(X,Y)=0\quad\Longleftrightarrow\quad X\perp\!\!\!\perp Y. $ For atomless margins the components reduce to $D$ and $R$, whereas in the presence of ties the corresponding classical identity $\tau^{*}=12D+24R$ can fail. The components arise from the Hoeffding projections of a symmetrised pair kernel. For the four strict/non-strict boundary versions $D_{\epsilon,\eta}$ and $R_{\epsilon,\eta}$, we establish the sharp comparisons $ 9\widetilde D\geq\sum_{\epsilon,\eta}D_{\epsilon,\eta}, \qquad 9\widetilde R\geq\sum_{\epsilon,\eta}R_{\epsilon,\eta}. $ Consequently, $\tau^{*}\geq0$ for every bivariate law, and the Bergsma–Dassios conjecture is settled: $\tau^{*}=0$ if and only if $X\perp\!\!\!\perp Y$. The boundary comparisons also yield the universal bound $\tau^{*}\geq(8/3)R$. Finite-table arguments, including an exact sum-of-squares certificate, establish the boundary inequalities, and weak-order quantisation transfers them to arbitrary laws. The factor $9$ in each comparison and the coefficient $24$ in $\tau^{*}\geq24\widetilde R$ are sharp. The usual permutation test is consistent against every fixed dependent alternative, without assumptions on the margins.

Large-scale multiple hypothesis testing is central to the analysis of high-throughput data, where controlling false discoveries is critical. Classical procedures typically rely on theoretical null distributions and often adjust for dependence among test statistics, but these approaches may be misleading when the empirical distribution of null statistics deviates from theoretical assumptions. Motivated by this observation, we investigate the role of the empirical cumulative distribution function (c.d.f.) of null test statistics in controlling the false discovery proportion (FDP). We first show that, under an oracle scenario where the empirical c.d.f. of the test statistics for all null hypotheses is known, FDP control can be achieved optimally regardless of the dependence structure, highlighting that explicit modeling of dependence may be unnecessary. Building on this insight, we propose an empirical c.d.f.-based FDP control (eFDP) method, implemented via a multivariate mixture model framework and a nonparametric estimation procedure for the empirical c.d.f.s, establish its asymptotic convergence, and construct an FDP control procedure that achieves asymptotic FDP control. Extensive simulations demonstrate that eFDP attains more accurate FDP control and higher power than existing approaches, particularly under strong dependence, and analysis of a high-dimensional breast cancer gene expression dataset confirms its practical utility.

We study the identity straight-through estimator (STE) for training a two-layer binary-activation network with hinge loss from the perspective of Statistical Learning Theory (SLT). Our central question is whether algorithmic stability can explain the statistical generalization of the estimator produced by the discontinuous STE training rule. In the saturated-output regime, the zero-initialized samplewise STE recursion is exactly the stochastic subgradient descent on the convex latent loss $(-yu^\top x)_+$. This representation makes a stability analysis possible. We derive an exact distance identity for two coupled updates and prove approximate non-expansiveness of the common-example map, with a quadratic defect only when the two latent margins straddle zero. We then obtain explicit $\ell_2$ on-average model-stability and generalization bounds, transferring stability isometrically from the latent vector to the full first-layer matrix. Combining stability with a standard optimization bound yields an explicit excess induced-risk guarantee and the rate $O(n^{-1/2})$ when $T=n^2$. Under margin separability, a complementary argument gives the optimal-order $O(R^2/(\gamma^2n))$ expected excess misclassification error for a randomized one-pass STE iterate and a corresponding majority-vote bound.

Clinical prediction models are increasingly fitted by penalized logistic regression, because collinearity or many candidate predictors makes maximum likelihood unstable or impossible. Calibration is then almost always assessed by a grouped goodness-of-fit test such as the Hosmer-Lemeshow test. We show that this combination is invalid. Under ridge regression the grouped standardized residuals acquire a non-centrality induced by shrinkage, so the reference distribution used in practice is wrong, and at the penalty that most improves the fitted probabilities the test rejects correctly specified models between 92 and 100 per cent of the time. We derive the corrected law and define the shrinkage-corrected Hosmer-Lemeshow test, which subtracts an estimate of that non-centrality, restoring the maximum likelihood reference exactly to first order, and is made valid by prepivoting at a power cost we measure. We also give the attenuation law governing what any such test can detect once the linear predictor must be estimated. In glaucoma diagnosis by confocal laser tomography, where the maximum likelihood estimate does not exist, the corrected test finds the evidence for misfit weaker by more than three orders of magnitude: the fitted risks are too flat rather than mis-ordered, so the model needs recalibration rather than rebuilding.

This work presents DPQBootstrap, a probabilistic resampling method for time series based on a Dirichlet quantile bootstrap and rank-based temporal reconstruction. The method aims to generate pseudo-series that preserve the main characteristics of the original series, including variability, quantiles, extreme values, and part of its temporal dependence. A simulation study compares DPQBootstrap with the Maximum Entropy Bootstrap implemented in the meboot package across eight simulation scenarios. The results show that DPQBootstrap achieves 106 wins over 86 for meboot according to the Interval Score, indicating a strong ability to preserve the statistical properties of the original time series. In addition, an empirical application was conducted within a Bayesian ARMA forecasting framework, with and without DPQBootstrap integration. The results indicate that incorporating DPQBootstrap can improve point forecast accuracy and the quality of predictive intervals, particularly when combined with appropriately specified ARMA models.

We study dynamic treatment regimes under contemporaneous confounding: at each stage, an unmeasured factor may affect both treatment and the next observed state, but has no further direct effect on later stages. From the observational distribution, the causal graph, and specified structural restrictions on possible next states, we construct at each state–treatment pair the set of transition probabilities compatible with this information. These local sets require no sensitivity parameter and can be combined by backward induction to obtain lower and upper bounds on the expected outcome under any given treatment regime. Our main result shows that these bounds are sharp: their endpoints are exactly the smallest and largest expected outcomes generated by causal models compatible with the same observational distribution, causal graph, and structural restrictions. The same backward-induction method gives a maximin rule for choosing treatments by maximizing the worst-case expected outcome. Thus, for this class of models with contemporaneous confounding, the framework generalizes the classical g-formula of \citet{Robins1986} for evaluating treatment regimes and the Q-learning framework of \citet{Murphy2003} for selecting them. When the local transition probabilities are identified, the two recursions reduce to these classical methods.

Massive datasets in modern machine learning have made data reduction a central challenge, particularly for clustering tasks where memory and computational constraints demand compact yet faithful summaries. A standard approach is to construct an \textit{$\epsilon$-coreset}: a small weighted subset that approximately preserves the clustering cost for every plausible choice of centers. For the \textit{$(k,z)$-clustering problem}, existing worst-case bounds on coreset size are essentially tight, ruling out substantially smaller coresets in general. However, such worst-case instances are often unrepresentative of real-world data. In this work, we show that significantly smaller coresets are possible under mild and natural assumptions on the underlying data distribution. We introduce a new correlated sampling framework, called determinantal sampling, based on a novel application of determinantal point processes. Using this framework, we obtain an efficiently constructible $\varepsilon$-coreset for $(k,z)$-clustering in $\mathbb R^d$ whose dependence on $1/\varepsilon$ has exponent strictly smaller than $2$ when $d$ is fixed. This improves over the worst-case $\varepsilon^{-2}$ barrier under our beyond-worst-case assumptions. To the best of our knowledge, this is the first result that provably surpasses these lower bounds through beyond-worst-case assumptions. Finally, we validate our approach on synthetic and real-world benchmark datasets, where it consistently achieves smaller coresets than existing state-of-the-art methods, even without explicitly enforcing the assumptions used in the analysis.

We introduce a similarity representation framework for robust heritability estimation in Genome-Wide Association Studies (GWAS). This problem parallels the signal-to-noise ratio estimation problem in linear models with a large number of predictors. Traditional fixed- and random-effects methods for heritability estimation often impose restrictive assumptions on regression coefficients or the design (genotype) matrix. These assumptions are usually violated by the heterogeneous effects of genetic variants (regression coefficients) that depend on the genotype distribution and the correlation among genotypes due to linkage disequilibrium. This leads to the non-robust estimation of heritability in practice. To overcome these limitations, we propose a SiMILarity rEpresentation method (SMILE) which models the relationship between the outcome similarity and genetic similarity through Gram matrices. SMILE represents genetic similarity using a weighted Gram matrix of genotypes, where a data-dependent weight matrix is used to disentangle the heterogeneous variant effects from the genotype distribution. SMILE includes the classical random-effects model as a special case and improves the fixed-effects model by not requiring accurate estimation of the precision matrix or the regression coefficients. We develop a scalable implementation for efficient analysis of large biobank GWAS data. Extensive simulations and the analysis of the UK Biobank data demonstrate the robustness of the proposed method over the existing methods across a range of genetic architectures, and show that SMILE provides a versatile approach for heritability estimation.

In many scientific disciplines, weak signals of interest are obscured by dominant nuisance signals that are several orders of magnitude stronger. Recovering these weak signals requires subtracting the dominant ones; however, this calibration process inherently distorts or partially suppresses the underlying signal of interest. To address this problem, we propose the use of normalizing flow models to reconstruct calibration-affected weak signals. By leveraging the statistical invariance of the target signals and assuming minimal initial suppression, our framework effectively recovers the lost signal components. We provide a comprehensive theoretical overview of this normalizing flow-based recovery method and demonstrate its efficacy using simulated data.

Dynamic causal modeling (DCM) estimates directed effective connectivity, while parametric empirical Bayes (PEB) supports group inference using subject-specific posterior summaries. Standard PEB relies on Gaussian models and continuous shrinkage, making it sensitive to atypical estimates and unable to distinguish negligible from nonzero effects. We develop a robust and sparse group-DCM extension combining a Student-t likelihood with a spike-and-slab prior using a nonlocal product-moment (pMOM) slab. A normal–gamma representation of the Student-t distribution yields weights that downweight atypical subject–parameter combinations. The pMOM slab vanishes at zero, sharpening coefficient selection and yielding inclusion probabilities. We propagate first-level posterior uncertainty through block-covariance pre-whitening and estimate the model using an EM–ReML algorithm that updates weights, inclusion probabilities, effects, and variance components. A simulation study showed that Student-t weighting provided the main protection against contamination, the nonlocal prior contributed most under strong sparsity, and their combination was most beneficial when contamination and sparsity occurred together. In an openly shared mixed-gambles fMRI application, we found mild heterogeneity, concentrated inclusion support on three intrinsic self-connections, and close directional agreement with standard SPM-PEB. Our framework therefore adds interpretable element-level robustness diagnostics and sparse coefficient selection to hierarchical DCM while retaining first-level uncertainty.

This study investigates the spatial relationships among housing-market appreciation, housing affordability, and automobile commuting to Toronto across 23 census metropolitan areas and municipalities in southern Ontario from 2016 to 2021. Utilizing Statistics Canada Census data, the analysis employed linear and quadratic ordinary least-squares regression, Global and Local Moran's I, and residual spatial diagnostics to assess geographic patterns in average dwelling values, owner shelter-cost burden, and lone-driver commuting. The study found that average dwelling values increased significantly throughout the region, maintaining a strong nonlinear relationship with distance from Toronto, which indicates a persistent metropolitan accessibility gradient. Commuter volumes also demonstrated pronounced nonlinear distance gradients; however, housing appreciation was not significantly correlated with percentage changes in commuting ($R^2$ = .045, p = .331), suggesting that the expansion of the housing market did not result in proportional growth in Toronto-bound automobile travel. The shelter-cost burden exhibited weaker distance relationships and greater residual spatial dependence, indicating localized affordability influences not fully explained by distance or dwelling values. Overall, the findings suggest an increasingly extensive regional housing market with spatially heterogeneous affordability and commuting outcomes, highlighting the importance of integrating housing, transportation, and regional planning.

Conditional dimension reduction (cDR) learns low-dimensional latent coordinates while accounting for observed covariates that represent known sources of variation in the data. Conditional Multidimensional Scaling (cMDS) is a cDR technique that works directly with dissimilarity data. Its standard squared-stress formulation, however, is sensitive to contaminated dissimilarity, since outliers can dominate the objective and distort the learned configuration. We proposed Robust Conditional Multidimensional Scaling (rcMDS) by replacing the squared-stress criterion with a Fair M-estimation objective. We developed a reweighted conditional SMACOF algorithm to optimize this objective. The proposed algorithm admits computationally tractable updates, and its stabilized objective values decrease monotonically and converge to a finite limit. Experiments on synthetic and real data show that the pro

Appeals to typicality are common in physics, but it is often unclear what it means for a physical state to be typical relative to a probability measure, and correspondingly unclear what a law that appeals to typicality asserts. Here we consider how one might characterize physical typicality using ideas from the theory of algorithmic randomness. As a concrete example, we show how taking a physical state to be typical relative to a computable measure when it is Martin-Löf random allows one to formulate the distribution postulate in Bohmian mechanics as a statistical constraining law of the theory. Using a toy model, we show how this constraint guarantees the standard Born statistics for computable experimental protocols. Algorithmic Bohmian mechanics (aBM) thus illustrates how algorithmic randomness may be used to provide precise content to a statistical law.

Investment performance is commonly presented either as a conventional cumulative-return chart, which fixes a historical starting date and traces performance forward, or as a trailing-return table, which fixes the current endpoint but reports only a small set of prespecified horizons. These two displays have complementary limitations: fixed-start comparisons are conditional on the selected origin, whereas trailing returns provide only discrete snapshots of the underlying fixed-endpoint return function. We present the Return-to-Present (RTP) curve as a continuous fixed-endpoint representation that brings these perspectives together by holding the evaluation date fixed while allowing the hypothetical historical purchase date to vary over the available history. Familiar 1-month, 3-month, 6-month, 1-year, and longer trailing returns therefore become selected points on a continuous curve. When multiple investments are overlaid, RTP directly displays entry-date sensitivity, persistent relative advantage, crossings, and the timing and magnitude of separation without requiring selection of a single historical origin. The same endpoint-based construction naturally accommodates investments with unequal inception dates, recurring purchases, and retrospective portfolio rotation decisions in which sale and replacement-purchase dates may differ. We illustrate these uses with real investment data and discuss its relationship to momentum. RTP does not define a new return measure; its contribution is a simple graphical organization of familiar realized returns for historical comparison and decision support rather than prediction or statistical inference.

In this paper, we develop and analyze techniques for recovering a linear image $Bx$ of an unknown signal $x$ from indirect noisy observation $\omega=Ax+\xi$. It is a priori known that $x\in \cX$, a given convex compact set, and that $x$ is $s$-sparse—has at most $s$ nonvanishing entries. The proposed estimates belong to a large family of recovery routines by $\ell_1$-minimization. However, unlike the classical result describing performance of such estimates, we do not make any special (and hard to check) assumptions about the sensing matrix $A$ such as nullspace or Restricted Isometry condition and the like. As a consequence, parameters of the estimates and the upper bounds on their risks are not available in a closed analytic form, but are delivered instead by efficient computation as solutions to explicit convex optimization problems.

We study the problem of low-rank matrix recovery from linear measurements via the global nonconvex landscape of a low-rank factored formulation of the matrix LASSO (nuclear-norm–regularized least-squares). If the landscape is benign, that is, has no bad local optima, then practical and scalable algorithms can compute good statistical estimates. Previous state-of-the-art landscape guarantees have typically assumed that the linear measurement operator has the restricted isometry property, that is, the operator is approximately an isometry over all low-rank matrices. This is an unrealistic assumption for many applications; in particular, when the individual measurement matrices are themselves low-rank, we typically have poor upper isometry constants. To overcome this, we establish new guarantees of a benign landscape under a weaker isometry condition: rather than requiring upper isometry over all low-rank matrices, we only require it over the linear low-rank tangent space to the low-rank ground truth matrix. To illustrate the utility of this result, we apply it to the problem of matrix recovery from random rank-one linear measurements; via high-probability concentration bounds on the random measurement operator, we prove a novel landscape guarantee with statistically near-optimal sample complexity and recovery error.

Count-valued variables arise in many scientific and applied settings, yet explicit structural models that allow full identification of causal DAGs from observational data remain limited. The Poisson branching structural causal model (PB-SCM) provides a count-valued analogue of linear structural equation models using binomial thinning and independent Poisson exogenous variables, but its causal DAG is generally only partially identifiable. Building on this framework, we propose the Poisson thinning structural equation model (PT-SEM), which replaces binomial thinning in PB-SCM with Poisson thinning and allows node-wise exogenous distributions from diverse count-distribution families. Under node-wise regularity conditions, we establish identifiability of the causal DAG, the thinning coefficients, and the node-wise exogenous distributions. The same identification analysis extends to binomial thinning, yielding full identifiability whenever every nonsink has non-Poisson exogenous noise. We further develop a structure learning algorithm that optimizes, via dynamic programming, a BIC score based on local likelihoods evaluated at plug-in moment estimates, and establish its consistency for DAG selection. Simulations demonstrate favorable performance in DAG recovery and thinning-coefficient estimation, and a real-data application illustrates the practical utility of PT-SEM.

Stochastic min-max optimization has attracted increasing attention due to its applications in modern machine learning, while existing theoretical studies mainly rely on the bounded variance assumption for stochastic gradients. Under heavy-tailed noise, where stochastic gradients only possess a finite $p$-th moment for $p\in(1,2]$, gradient clipping or normalization is commonly believed to be necessary to guarantee convergence. In this work, we revisit stochastic min-max optimization under heavy-tailed noise and provide a comprehensive theoretical study of stochastic gradient descent ascent (SGDA). We first show that vanilla SGDA, without any modification to its update rule, can converge under heavy-tailed noise in both nonconvex-strongly-concave (NC-SC) and nonconvex-concave (NC-C) settings, establishing the first convergence guarantees for SGDA in these regimes. Beyond unregularized problems, we further investigate regularized stochastic min-max optimization, where directly incorporating gradient normalization into proximal updates is nontrivial due to the incompatibility between normalization and proximal structures. We overcome this difficulty by developing new clipping-free algorithms, i.e., Stoc-TRGDAM and Stoc-TRGDmax, and they both can achieve the optimal dependence on the target accuracy without using gradient clipping.

Empiric antibiotic therapy for suspected ESBL-producing Enterobacteriaceae must be selected 48-72 hours before culture results, forcing clinicians to choose between undertreating resistant infections and overusing carbapenems that drive further resistance. We developed a cost-sensitive XGBoost model predicting an ESBL phenotype (resistance to ceftriaxone, ceftazidime, cefepime or piperacillin-tazobactam) at culture ordering using 45 pre-culture EHR features across 132,955 cultures from 72,217 patients at 12 hospitals (14.41% with the ESBL phenotype). Cultures were partitioned at the patient level. At 90% sensitivity, the model achieved 95.8% NPV, reducing post-test ESBL probability to 4.2%, a threshold that may support safe carbapenem-sparing in non-ICU settings, while sparing 307 of every 1,000 cultures an unnecessary broad-spectrum course at the cost of 14 missed ESBL cases per 1,000. SHAP analysis identified prior ESBL colonization as the dominant predictor, ahead of prior organism burden and neighborhood deprivation; removing deprivation features caused minimal performance loss ($\Delta\text{AUROC} = -0.020$), enabling equitable bedside deployment. Discrimination was unchanged under a strict IDSA ESBL-E definition (AUROC 0.766), with specimen type added as a predictor (0.764) and without any class-imbalance correction (0.762), and ranged from 0.71 to 0.78 across organism strata.

Existing unlearning approaches typically rely on post hoc weight adaptation or distillation, leading to duplicated memory costs, degraded generalization, and limited scalability. In this work, we introduce ERASE, Erasure via Reconstructive Adversarial Signal Editing, a framework for on-the-go forgetting that suppresses the observable influence of private data without modifying model weights. ERASE leverages structured, class-conditioned input perturbations to induce selective forgetting during inference, eliminating the need for retraining, fine-tuning, or model copies. We rigorously characterize sufficient conditions when ERASE provably achieves functional forgetting of designated subclasses while preserving predictions across other subclasses within the same superclass. This analysis offers a principled foundation for inference-time forgetting under mild regularity assumptions. Across diverse architectures and benchmark datasets, ERASE maintains the best observed balance between forgetting efficacy, computational efficiency, and retention fidelity over recent unlearning-based methods. By reimagining data removal as forgetting without unlearning, our work establishes a scalable, regulation-aligned pathway for continual, privacy-conscious learning.

Optimization-based simultaneous localization and mapping (SLAM) makes it possible to reduce accumulated navigation errors of sensing platforms by returning to known areas (loop closure). In this paper, we present an approach to combine probabilistic data association (PDA) with optimization-based SLAM. Instead of associating a single measurement with each landmark, we follow the PDA paradigm from the multiobject tracking community. In particular, in a processing stage performed in addition to the nonlinear least-squares solver of optimization-based SLAM, our method (i) assigns multiple measurements to landmarks probabilistically, (ii) computes the mean and covariance of landmark distributions via moment matching by taking multiple measurement-to-landmark associations into account, and (iii) establishes a virtual landmark measurement and a corresponding linear-Gaussian measurement model that leads to the mean and covariance matrix as moment-matching PDA in (ii). By converting the PDA update step into an equivalent linear-Gaussian measurement update step, PDA can be performed effectively within any optimization-based SLAM method. Our preliminary numerical evaluation in a scenario with false negatives and false positives indicates that incremental smoothing and mapping 2 (iSAM2), combined with the proposed PDA approach, can improve agent localization performance compared to conventional iSAM2.

We study extremal absolute central moments of Gaussian quadratic forms under a fixed Frobenius norm. For a nonzero real symmetric matrix $M$ and $G\sim N(0,I_n)$, we construct an explicit centered difference of Gamma variables with the same mean, variance, and third centered moment as $G^{\mathsf T}MG-\operatorname{tr}M$. After normalization, replacing the quadratic form by this Gamma difference does not decrease $\mathbb{E} f$ for every $C^2$ test function $f$ such that $f''$ is convex and $f$, $f'$, and $f''$ have polynomial growth. In particular, it gives an explicit upper bound for every absolute moment of order $p\ge3$. We then prove that, for every $p\ge4$, this bound is maximized by the centered square $g^2-1$ of a single standard Gaussian variable $g$. The resulting sharp inequality is \[ \bigl\|G^{\mathsf T}MG-\operatorname{tr}M\bigr\|_p \le \|g^2-1\|_p\,\|M\|_{\mathrm F}, \] with equality if and only if $M$ has rank one.

This paper develops fixed-smoothing (fixed-b, fixed-K) inference methods for time-series quantile regression that are robust to heteroskedasticity and autocorrelation. Our approach is uniformly valid over quantile levels and accounts for dependence both over time and across quantiles. It enables the construction of uniform confidence bands, Wald, and Sup-t tests for joint hypotheses, and tests of shape restrictions, providing a unified framework for assessing heterogeneity in quantile effects. A key challenge is that, under weak dependence, uniform inference for quantile regression processes is generally non-pivotal because the limiting distributions depend on the long-run covariance structure across quantiles. To address this issue, we develop two complementary approaches. The uniform-in-$\tau$ method estimates the covariance structure and simulates the non-pivotal limiting distribution. For certain tests involving a finite collection of quantile levels, the stack-Wald method delivers pivotal fixed-smoothing inference. We establish the asymptotic validity of both approaches. Simulation results show that the proposed methods substantially improve size control relative to existing HAC-based procedures while maintaining good power. An application to predictive quantile regressions for stock returns reveals substantial heterogeneity in predictive effects across both quantiles and forecast horizons.

Learning with class-conditional label noise often relies on a transition model from latent clean classes to observed annotations. Forward correction embeds this transition in the likelihood, yet finite-sample networks may still memorize corrupted labels. The corrected likelihood also induces a reverse posterior over the clean classes that could explain each annotation. When its leading class differs from the annotation, the model and transition matrix provide evidence against that annotation, but the leading alternatives can remain nearly tied. We introduce Selective Posterior Margin Regularization (SPMR), which preserves the Forward objective and converts this disagreement into a graded update on the clean classifier. SPMR selects the leading reverse-posterior class, scales a detached pairwise margin by the separation between the two leading posterior classes, and assigns correspondingly little influence to diffuse conflicts. The gap factorizes into transition- adjusted pairwise separation and the posterior mass carried by the leading pair. The active margin follows the locally minimum-norm logit direction that enlarges the selected pairwise margin. Across five known-transition benchmarks, SPMR improves full-length Forward by 2.5-7.0 percentage points and remains 0.7-2.5 percentage points above Forward with Mixup and early stopping. Matched interventions support distinct gains from the posterior-space coefficient, transition-adjusted target, and pairwise action. The same design transfers to estimated transitions, human annotations, architectural changes, and stronger Forward recipes. The formulation uses latent-class evidence already available inside Forward correction without promoting every posterior conflict to a corrected label.

Let $\pi(\mathrm{d} x)\propto e^{-U(x)}\, \mathrm{d} x$ on $\mathbb{R}^d$, where $U$ is continuously differentiable and $m$-strongly convex with a globally $L$-Lipschitz gradient, $0<m\leq L<\infty$, and $\kappa=L/m$. Fixed-step Metropolis-adjusted Langevin algorithm (MALA) has known warm-start mixing-time upper bounds of order $\kappa\sqrt d$, up to logarithmic factors. A spectral-gap lower bound at the corresponding scale $(\kappa \sqrt{d})^{-1}$ would give an upper bound of order $\kappa \sqrt{d}$ on the Monte Carlo asymptotic variance relative to independent sampling, uniformly over all square-integrable functions. However, when $\kappa$ is bounded away from~1, the best fixed-step spectral gap that can be guaranteed uniformly over this target class is at most of order $\max\{\log(\kappa d)/(\kappa d), e^{-cd}\}$ for some positive universal constant~$c$. We show that uniform randomization of the step size improves this worst-case guarantee. At each iteration, the algorithm draws $h\sim\operatorname{Unif}(0,H)$ and performs one ordinary MALA transition. Choosing $H$ of order $[L\sqrt{d(1+\log d+\log\kappa)}]^{-1}$ yields a right spectral-gap lower bound of order \[ \frac{1}{\kappa\sqrt{d(1+\log d+\log\kappa)}}, \] uniformly over the target class. Thus, given $\kappa > 1$, for all square-integrable functions, the ratio of the Monte Carlo asymptotic variance relative to independence sampling has an upper bound of order $\sqrt{d \log d}$. This contrasts with fixed-MALA, where the ratio can be as bad as $d/\log d$ in thew worst-case scenario. The spectral gap also gives geometric convergence of the lazy kernel from every initial density in $L^2(\pi)$, central limit theorems, and nonstationary mean-square error bounds. This work was developed with substantial assistance from ChatGPT.