arXiv subjects

Ashwin Pananjady

Publications and source records attributed to Ashwin Pananjady.

At least 19 recordsLinked to original sources

arXiv2026

Signal recovery in the polychromatic computed tomography model: Injectivity and complexity

We consider a nonlinear model motivated by polychromatic computed tomography (CT). Here, $W$ distinct $d$-dimensional signals $x^*_1, \ldots, x^*_W \in \mathbb{R}^d$ must be recovered from $n$ measurements $(a_i, y_i)_{i = 1}^n$ that obey the nonlinear model $\mathbb{E}[y_i|a_i] = h(\langle a_i, x^*_1 \rangle, \ldots, \langle a_i, x^*_W \rangle)$, where $h: \mathbb{R}^W \to \mathbb{R}$ is a known nonlinearity that models a certain type of exponential attenuation law. Even when there is no noise in the measurements, the sample size $n$ (for any measurement ensemble $\{a_i\}_{i = 1}^n$) must exceed the number of unknowns $Wd$ to guarantee that the underlying signals are identifiable. We construct a measurement ensemble that ensures perfect signal recovery almost surely provided $n \geq Wd + W - 1$, thereby isolating the injectivity threshold up to an additive factor $W - 1$. We also study computational complexity of signal recovery in this model with a general measurement ensemble $\{a_i\}$. We show that if $W \geq 2$, then there is a measurement ensemble for which deciding whether there exist signals consistent with the measurements is NP-hard. In particular, this implies that polychromatic, multimaterial CT reconstruction is NP-hard in general. This finding stands in sharp contrast to the single-material setting, for which a polynomial-time algorithm can provably perform signal recovery for any measurement ensemble.

eess.IV↗

arXiv2026

Next-token functional estimation

Suppose we observe the first $n$ points of a sequence of random variables having length $n+1$, and wish to estimate a functional of the unobserved final point and the empirical measure of the $n$ observed training points. Such next-token functionals include the probability that the next token is novel (also known as the surprise probability), the tail probability of the minimum distance between the next token and training points, and the test error of a classifier trained on the observed points. All of these quantities are classically estimated by the leave-one-out method, which is inconsistent under temporal dependence. We propose a leave-a-window-out estimator, which deletes a window of length $τ$ after each index before forming the empirical measure and reduces to leave-one-out at $τ= 1$. Under natural assumptions, we show that the error of our estimator decays at a parametric rate for any stationary $β$-mixing process that also admits a Marton coupling. Our results thus cover several natural functionals on a large class of stochastic processes. We complement these upper bounds with a sharp minimax lower bound for estimating the surprise probability on mixing Markov chains. Simulations on Markov chains, moving-average processes, and autoregressive processes show that our estimator succeeds in many scenarios where leave-one-out and add-constant baselines fail.

stat.ML↗

arXiv2026

Toward individual-level calibration in affect recognition with perceptual adjustment queries

Behavioral tasks measuring facial affect perception assume that identical stimuli impose equivalent perceptual difficulty across participants. However, this assumption is systematically violated by individual differences in perceptual sensitivity. Using an affective perception task as our testbed, we propose a framework to normalize for perceptual difficulty that directly estimates each participant's Just Noticeable Difference (JND) along the facial affect spectrum via cognitively lightweight perceptual adjustment queries (PAQs). We use these PAQ-inferred JNDs to re-express stimulus distances, constructing difficulty-equated tasks in perceptual space. We validate the framework in a Two-Alternative Forced-Choice (2AFC) task using two complementary behavioral measures: binary metacognitive difficulty judgments and response time variance decomposition. We find that PAQ calibration significantly equalizes perceived task difficulty at an individual level when compared to both the non-calibrated baseline and population-level Weibull calibration, while also reducing mean response time and between-subject variance in response time. These results establish PAQ as a principled and practical instrument for individualized perceptual calibration in facial affect recognition.

cs.LG↗

arXiv2026

Leave a Window Out: Modifying the Jackknife for Predictive Inference in Time Series

Conformal prediction methods enjoy strong theoretical and empirical predictive inference performance, provided the data is exchangeable and is treated symmetrically during training. However, these assumptions are impractical in many settings, such as time series, where temporal dependence violates exchangeability and it is preferable to use predictors that leverage dependence by treating data asymmetrically. Recent work shows that split conformal prediction is robust to these issues, but sample splitting can reduce accuracy, motivating the study of methods that do not rely on data splitting in the time series setting. In this work, we show that the vanilla leave-one-out jackknife can suffer arbitrary loss of coverage even in canonical time series models with mild temporal dependence. As a remedy, we propose a modification tailored to such settings, which we term the leave-a-window-out (LWO) method, and show that it can achieve valid coverage provided that the model-fitting procedure satisfies mild stability properties. Our proofs are based on quantifying the degree to which the data departs from cyclic exchangeability, which we introduce new coefficients to measure. Experiments on time series demonstrate that our method often enjoys valid coverage when the vanilla jackknife fails to cover, while producing much narrower intervals than split conformal prediction.

stat.ML↗

arXiv2026

Instance-optimal stochastic convex optimization: Can we improve upon sample-average and robust stochastic approximation?

We study the unconstrained minimization of a smooth and strongly convex population loss function under a stochastic oracle that introduces both additive and multiplicative noise; this is a canonical and widely-studied setting that arises across operations research, signal processing, and machine learning. We begin by showing that standard approaches such as sample average approximation and robust (or averaged) stochastic approximation can lead to suboptimal -- and in some cases arbitrarily poor -- performance with realistic finite sample sizes. In contrast, we demonstrate that a carefully designed variance reduction strategy, which we term VISOR for short, can significantly outperform these approaches while using the same sample size. Our upper bounds are complemented by finite-sample, information-theoretic local minimax lower bounds, which highlight fundamental, instance-dependent factors that govern the performance of any estimator. Taken together, these results demonstrate that an accelerated variant of VISOR is instance-optimal, achieving the best possible sample complexity up to logarithmic factors while also attaining optimal oracle complexity. We apply our theory to generalized linear models and improve upon classical results. In particular, we obtain the best-known non-asymptotic, instance-dependent generalization error bounds for stochastic methods, even in linear regression.

math.OC↗

arXiv2026

Accurate, provable and fast polychromatic tomographic reconstruction: A variational inequality approach

We consider the problem of signal reconstruction for computed tomography (CT) under a nonlinear forward model that accounts for exponential signal attenuation, a polychromatic X-ray source, general measurement noise (e.g., Poisson shot noise), and observations acquired over multiple wavelength windows. We develop a simple iterative algorithm for single-material reconstruction, which we call EXACT (EXtragradient Algorithm for Computed Tomography), based on formulating our estimate as the fixed point of a monotone variational inequality. We prove guarantees on the statistical and computational performance of EXACT under realistic assumptions on the measurement process. We also consider a recently introduced variant of this model with Gaussian measurements and present sample and iteration complexity bounds for EXACT that improve upon those of existing algorithms. We apply our EXACT algorithm to a CT phantom image recovery task and show that it often requires fewer X-ray views, lower source intensity, and less computation time to achieve reconstruction quality similar to existing methods. Code is available at https://github.com/voilalab/exact.

eess.IV↗

arXiv2026

Perfusion Imaging and Single Material Reconstruction in Polychromatic Photon Counting CT

Background: Perfusion computed tomography (CT) images the dynamics of a contrast agent through the body over time, and is one of the highest X-ray dose scans in medical imaging. Recently, a theoretically justified reconstruction algorithm based on a monotone variational inequality (VI) was proposed for single material polychromatic photon-counting CT, and showed promising early results at low-dose imaging. Purpose: We adapt this reconstruction algorithm for perfusion CT, to reconstruct the concentration map of the contrast agent while the static background tissue is assumed known; we call our method VI-PRISM (VI-based PeRfusion Imaging and Single Material reconstruction). We evaluate its potential for dose-reduced perfusion CT, using a digital phantom with water and iodine of varying concentration. Methods: Simulated iodine concentrations range from 0.05 to 2.5 mg/ml. The simulated X-ray source emits photons up to 100 keV, with average intensity ranging from $10^5$ down to $10^2$ photons per detector element. The number of tomographic projections was varied from 984 down to 8 to characterize the tradeoff in photon allocation between views and intensity. Results: We compare VI-PRISM against filtered back-projection (FBP), and find that VI-PRISM recovers iodine concentration with error below 0.4 mg/ml at all source intensity levels tested. Even with a dose reduction between 10x and 100x compared to FBP, VI-PRISM exhibits reconstruction quality on par with FBP. Conclusion: Across all photon budgets and angular sampling densities tested, VI-PRISM achieved consistently lower RMSE, reduced noise, and higher SNR compared to filtered back-projection. Even in extremely photon-limited and sparsely sampled regimes, VI-PRISM recovered iodine concentrations with errors below 0.4 mg/ml, showing that VI-PRISM can support accurate and dose-efficient perfusion imaging in photon-counting CT.

physics.med-ph↗

arXiv2026

Predictive inference for time series: why is split conformal effective despite temporal dependence?

We consider the problem of uncertainty quantification for prediction in a time series: if we use past data to forecast the next time point, can we provide valid prediction intervals around our forecasts? To avoid placing distributional assumptions on the data, in recent years the conformal prediction method has been a popular approach for predictive inference, since it provides distribution-free coverage for any iid or exchangeable data distribution. However, in the time series setting, the strong empirical performance of conformal prediction methods is not well understood, since even short-range temporal dependence is a strong violation of the exchangeability assumption. Using predictors with "memory" -- i.e., predictors that utilize past observations, such as autoregressive models -- further exacerbates this problem. In this work, we examine the theoretical properties of split conformal prediction in the time series setting, including the case where predictors may have memory. Our results bound the loss of coverage of these methods in terms of a new "switch coefficient", measuring the extent to which temporal dependence within the time series creates violations of exchangeability. Our characterization of the coverage probability is sharp over the class of stationary, $β$-mixing processes. Along the way, we introduce tools that may prove useful in analyzing other predictive inference methods for dependent data.

stat.ML↗

arXiv2026

Multiscale replay: A robust algorithm for stochastic variational inequalities with a Markovian buffer

We introduce the Multiscale Experience Replay (MER) algorithm for solving a class of stochastic variational inequalities (VIs) in settings where samples are generated from a Markov chain and we have access to a memory buffer to store them. Rather than uniformly sampling from the buffer, MER utilizes a multi-scale sampling scheme to emulate the behavior of VI algorithms designed for independent and identically distributed samples, overcoming bias in the de facto serial scheme and thereby accelerating convergence. Notably, unlike standard sample-skipping variants of serial algorithms, MER is robust in that it achieves this acceleration in iteration complexity whenever possible, and without requiring knowledge of the mixing time of the Markov chain. We also discuss applications of MER, particularly in policy evaluation with temporal difference learning and in training generalized linear models with dependent data.

math.OC↗

arXiv2025

Efficient reductions from a Gaussian source with applications to statistical-computational tradeoffs

Given a single observation from a Gaussian distribution with unknown mean $θ$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_θ$ uniformly for all $θ$ in a parameter set. We leverage our technique to establish reduction-based computational lower bounds for several canonical high-dimensional statistical models under widely-believed conjectures in average-case complexity. In particular, we cover cases in which: 1. $Q_θ$ is a general location model with non-Gaussian distribution, including both light-tailed examples (e.g., generalized normal distributions) and heavy-tailed ones (e.g., Student's $t$-distributions). As a consequence, we show that computational lower bounds proved for spiked tensor PCA with Gaussian noise are universal, in that they extend to other non-Gaussian noise distributions within our class. 2. $Q_θ$ is a normal distribution with mean $f(θ)$ for a general, smooth, and nonlinear link function $f:\mathbb{R} \rightarrow \mathbb{R}$. Using this reduction, we construct a reduction from symmetric mixtures of linear regressions to generalized linear models with link function $f$, and establish computational lower bounds for solving the $k$-sparse generalized linear model when $f$ is an even function. This result constitutes the first reduction-based confirmation of a $k$-to-$k^2$ statistical-to-computational gap in $k$-sparse phase retrieval, resolving a conjecture posed by Cai et al. (2016). As a second application, we construct a reduction from the sparse rank-1 submatrix model to the planted submatrix model, establishing a pointwise correspondence between the phase diagrams of the two models that faithfully preserves regions of computational hardness and tractability.

math.ST↗

arXiv2025

State evolution beyond first-order methods I: Rigorous predictions and finite-sample guarantees

We develop a toolbox for exact analysis of iterative algorithms on a class of high-dimensional nonconvex optimization problems with random data. While prior work has shown that low-dimensional statistics of (generalized) first-order methods can be predicted by a deterministic recursion known as state evolution, our focus is on developing such a prediction for a more general class of algorithms. We provide a state evolution for any method whose iterations are given by (possibly interleaved) first-order and saddle point updates, showing two main results. First, we establish a rigorous state evolution prediction that holds even when the updates are not coordinate-wise separable. Second, we establish finite-sample guarantees bounding the deviation of the empirical updates from the established state evolution. In the process, we develop a technical toolkit that may prove useful in related problems. One component of this toolkit is a general Hilbert space lifting technique to prove existence and uniqueness of a convenient parameterization of the state evolution. Another component of the toolkit combines a generic application of Bolthausen's conditioning method with a sequential variant of Gordon's Gaussian comparison inequality, and provides additional ingredients that enable a general finite-sample analysis.

math.ST↗

arXiv2025

Estimating stationary mass, frequency by frequency

Suppose we observe a trajectory of length $n$ from an exponentially $α$-mixing stochastic process over a finite but potentially large state space. We consider the problem of estimating the probability mass placed by the stationary distribution of any such process on elements that occur with a certain frequency in the observed sequence. We estimate this vector of probabilities in total variation distance, showing universal consistency in $n$ and recovering known results for i.i.d. sequences as special cases. Our proposed methodology -- implementable in linear time -- carefully combines the plug-in (or empirical) estimator with a recently-proposed modification of the Good--Turing estimator called WingIt, which was originally developed for Markovian sequences. En route to controlling the error of our estimator, we develop new performance bounds on WingIt and the plug-in estimator for exponentially $α$-mixing stochastic processes. Importantly, the extensively used method of Poissonization can no longer be applied in our non i.i.d. setting, and so we develop complementary tools -- including concentration inequalities for a natural self-normalized statistic of mixing sequences -- that may prove independently useful in the design and analysis of estimators for related problems. Simulation studies corroborate our theoretical findings.

stat.ML↗

arXiv2024

Just Wing It: Near-Optimal Estimation of Missing Mass in a Markovian Sequence

We study the problem of estimating the stationary mass -- also called the unigram mass -- that is missing from a single trajectory of a discrete-time, ergodic Markov chain. This problem has several applications -- for example, estimating the stationary missing mass is critical for accurately smoothing probability estimates in sequence models. While the classical Good--Turing estimator from the 1950s has appealing properties for i.i.d. data, it is known to be biased in the Markovian setting, and other heuristic estimators do not come equipped with guarantees. Operating in the general setting in which the size of the state space may be much larger than the length $n$ of the trajectory, we develop a linear-runtime estimator called Windowed Good--Turing (WingIt) and show that its risk decays as $\widetilde{O}(\mathsf{T_{mix}}/n)$, where $\mathsf{T_{mix}}$ denotes the mixing time of the chain in total variation distance. Notably, this rate is independent of the size of the state space and minimax-optimal up to a logarithmic factor in $n / \mathsf{T_{mix}}$. We also present an upper bound on the variance of the missing mass random variable, which may be of independent interest. We extend our estimator to approximate the stationary mass placed on elements occurring with small frequency in the trajectory. Finally, we demonstrate the efficacy of our estimators both in simulations on canonical chains and on sequences constructed from natural language text.

stat.ML↗

arXiv2024

Alternating minimization for generalized rank one matrix sensing: Sharp predictions from a random initialization

We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study the convergence properties of a natural alternating update rule for this nonconvex optimization problem starting from a random initialization. We show sharp convergence guarantees for a sample-split version of the algorithm by deriving a deterministic recursion that is accurate even in high-dimensional problems. Notably, while the infinite-sample population update is uninformative and suggests exact recovery in a single step, the algorithm -- and our deterministic prediction -- converges geometrically fast from a random initialization. Our sharp, non-asymptotic analysis also exposes several other fine-grained properties of this problem, including how the nonlinearity and noise level affect convergence behavior. On a technical level, our results are enabled by showing that the empirical error recursion can be predicted by our deterministic sequence within fluctuations of the order $n^{-1/2}$ when each iteration is run with $n$ observations. Our technique leverages leave-one-out tools originating in the literature on high-dimensional $M$-estimation and provides an avenue for sharply analyzing higher-order iterative algorithms from a random initialization in other high-dimensional optimization problems with random data.

math.OC↗

arXiv2024

Computationally efficient reductions between some statistical models

We study the problem of approximately transforming a sample from a source statistical model to a sample from a target statistical model without knowing the parameters of the source model, and construct several computationally efficient such reductions between canonical statistical experiments. In particular, we provide computationally efficient procedures that approximately reduce uniform, Erlang, and Laplace location models to general target families. We illustrate our methodology by establishing nonasymptotic reductions between some canonical high-dimensional problems, spanning mixtures of experts, phase retrieval, and signal denoising. Notably, the reductions are structure-preserving and can accommodate missing data. We also point to a possible application in transforming one differentially private mechanism to another.

math.ST↗

arXiv2024

Optimal and instance-dependent guarantees for Markovian linear stochastic approximation

We study stochastic approximation procedures for approximately solving a $d$-dimensional linear fixed point equation based on observing a trajectory of length $n$ from an ergodic Markov chain. We first exhibit a non-asymptotic bound of the order $t_{\mathrm{mix}} \tfrac{d}{n}$ on the squared error of the last iterate of a standard scheme, where $t_{\mathrm{mix}}$ is a mixing time. We then prove a non-asymptotic instance-dependent bound on a suitably averaged sequence of iterates, with a leading term that matches the local asymptotic minimax limit, including sharp dependence on the parameters $(d, t_{\mathrm{mix}})$ in the higher order terms. We complement these upper bounds with a non-asymptotic minimax lower bound that establishes the instance-optimality of the averaged SA estimator. We derive corollaries of these results for policy evaluation with Markov noise -- covering the TD($λ$) family of algorithms for all $λ\in [0, 1)$ -- and linear autoregressive models. Our instance-dependent characterizations open the door to the design of fine-grained model selection procedures for hyperparameter tuning (e.g., choosing the value of $λ$ when running the TD($λ$) algorithm).

math.OC↗

arXiv2024

Hyperparameter tuning via trajectory predictions: Stochastic prox-linear methods in matrix sensing

Motivated by the desire to understand stochastic algorithms for nonconvex optimization that are robust to their hyperparameter choices, we analyze a mini-batched prox-linear iterative algorithm for the problem of recovering an unknown rank-1 matrix from rank-1 Gaussian measurements corrupted by noise. We derive a deterministic recursion that predicts the error of this method and show, using a non-asymptotic framework, that this prediction is accurate for any batch-size and a large range of step-sizes. In particular, our analysis reveals that this method, though stochastic, converges linearly from a local initialization with a fixed step-size to a statistical error floor. Our analysis also exposes how the batch-size, step-size, and noise level affect the (linear) convergence rate and the eventual statistical estimation error, and we demonstrate how to use our deterministic predictions to perform hyperparameter tuning (e.g. step-size and batch-size selection) without ever running the method. On a technical level, our analysis is enabled in part by showing that the fluctuations of the empirical iterates around our deterministic predictions scale with the error of the previous iterate.

math.OC↗

arXiv2023

Do algorithms and barriers for sparse principal component analysis extend to other structured settings?

We study a principal component analysis problem under the spiked Wishart model in which the structure in the signal is captured by a class of union-of-subspace models. This general class includes vanilla sparse PCA as well as its variants with graph sparsity. With the goal of studying these problems under a unified statistical and computational lens, we establish fundamental limits that depend on the geometry of the problem instance, and show that a natural projected power method exhibits local convergence to the statistically near-optimal neighborhood of the solution. We complement these results with end-to-end analyses of two important special cases given by path and tree sparsity in a general basis, showing initialization methods and matching evidence of computational hardness. Overall, our results indicate that several of the phenomena observed for vanilla sparse PCA extend in a natural fashion to its structured counterparts.

stat.ML↗