The automated detection of cancerous tumors has attracted interest mainly during the last decade, due to the necessity of early and efficient diagnosis that will lead to the most effective possible treatment of the impending risk. Several machine learning and artificial intelligence methodologies has been employed aiming to provide trustworthy helping tools that will contribute efficiently to this attempt. In this article, we present a low-complexity convolutional neural network architecture for tumor classification enhanced by a robust image augmentation methodology. The effectiveness of the presented deep learning model has been investigated based on 3 datasets containing brain, kidney and lung images, showing remarkable diagnostic efficiency with classification accuracies of 99.33%, 100% and 99.7% for the 3 datasets respectively. The impact of the augmentation preprocessing step has also been extensively examined using 4 evaluation measures. The proposed low-complexity scheme, in contrast to other models in the literature, renders our model quite robust to cases of overfitting that typically accompany small datasets frequently encountered in medical classification challenges. Finally, the model can be easily re-trained in case additional volume images are included, as its simplistic architecture does not impose a significant computational burden.
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Treatment-covariate interaction tests are commonly applied by researchers to examine whether the treatment effect varies across patient subgroups defined by baseline characteristics. The objective of this study is to explore treatment-covariate interaction tests involving covariate-adaptive randomization. Without assuming a parametric data generation model, we investigate usual interaction tests and observe that they tend to be conservative: specifically, their limiting rejection probabilities under the null hypothesis do not exceed the nominal level and are typically strictly lower than it. To address this problem, we propose modifications to the usual tests to obtain corresponding exact tests. Moreover, we introduce a novel class of stratified-adjusted interaction tests that are simple, broadly applicable, and more powerful than the usual and modified tests. Our findings are relevant to two types of interaction tests: one involving stratification covariates and the other involving additional covariates that are not used for randomization.
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical analysis, complexity theory, quantum algorithms, etc. The one, most relevant for us, is the amplification of approximation method: it allows to construct approximations of higher degree $M$ and better accuracy from the approximations of degree $m$.
Modeling symptom progression to identify informative subjects for a new Huntington's disease clinical trial is problematic since time to diagnosis, a key covariate, can be heavily censored. Imputation is an appealing strategy where censored covariates are replaced with their conditional means, but existing methods saw over 200% bias under heavy censoring. Calculating these conditional means well requires estimating and then integrating over the survival function of the censored covariate from the censored value to infinity. To estimate the survival function flexibly, existing methods use the semiparametric Cox model with Breslow's estimator, leaving the integrand for the conditional means (the estimated survival function) undefined beyond the observed data. The integral is then estimated up to the largest observed covariate value, and this approximation can cut off the tail of the survival function and lead to severe bias, particularly under heavy censoring. We propose a hybrid approach that splices together the semiparametric survival estimator with a parametric extension, making it possible to approximate the integral up to infinity. In simulation studies, our proposed approach of extrapolation then imputation substantially reduces the bias seen with existing imputation methods, even when the parametric extension was misspecified. We further demonstrate how imputing with corrected conditional means helps to prioritize patients for future clinical trials.
We consider linear problems in the worst case setting. That is, given a linear operator and a pool of admissible linear measurements, we want to approximate the values of the operator uniformly on a convex and balanced set by means of algorithms that use at most $n$ such measurements. It is known that, in general, linear algorithms do not yield an optimal approximation. However, as we show in this paper, an optimal approximation can always be obtained with a homogeneous algorithm. This is of interest to us for two reasons. First, the homogeneity allows us to extend any error bound on the unit ball to the full input space. Second, homogeneous algorithms are better suited to tackle problems on cones, a scenario that is far less understood than the classical situation of balls. We illustrate our results by several examples.
Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from sequential simulation using neural network-based conditional density estimators by minimizing a specific loss function. The SNPE method proposed by Lueckmann et al. (2017) used a calibration kernel to boost the sample weights around the observed data, resulting in a concentrated loss function. However, the use of calibration kernels may increase the variances of both the empirical loss and its gradient, making the training inefficient. To improve the stability of SNPE, this paper proposes to use an adaptive calibration kernel and several variance reduction techniques. The proposed method greatly speeds up the process of training, and provides a better approximation of the posterior than the original SNPE method and some existing competitors as confirmed by numerical experiments.
We consider the problem of sequential change detection, where the goal is to design a scheme for detecting any changes in a parameter or functional $\theta$ of the data stream distribution that has small detection delay, but guarantees control on the frequency of false alarms in the absence of changes. In this paper, we describe a simple reduction from sequential change detection to sequential estimation using confidence sequences: we begin a new $(1-\alpha)$-confidence sequence at each time step, and proclaim a change when the intersection of all active confidence sequences becomes empty. We prove that the average run length is at least $1/\alpha$, resulting in a change detection scheme with minimal structural assumptions~(thus allowing for possibly dependent observations, and nonparametric distribution classes), but strong guarantees. Our approach bears an interesting parallel with the reduction from change detection to sequential testing of Lorden (1971) and the e-detector of Shin et al. (2022).
We resurrect the infamous harmonic mean estimator for computing the marginal likelihood (Bayesian evidence) and solve its problematic large variance. The marginal likelihood is a key component of Bayesian model selection to evaluate model posterior probabilities; however, its computation is challenging. The original harmonic mean estimator, first proposed by Newton and Raftery in 1994, involves computing the harmonic mean of the likelihood given samples from the posterior. It was immediately realised that the original estimator can fail catastrophically since its variance can become very large (possibly not finite). A number of variants of the harmonic mean estimator have been proposed to address this issue although none have proven fully satisfactory. We present the \emph{learnt harmonic mean estimator}, a variant of the original estimator that solves its large variance problem. This is achieved by interpreting the harmonic mean estimator as importance sampling and introducing a new target distribution. The new target distribution is learned to approximate the optimal but inaccessible target, while minimising the variance of the resulting estimator. Since the estimator requires samples of the posterior only, it is agnostic to the sampling strategy used. We validate the estimator on a variety of numerical experiments, including a number of pathological examples where the original harmonic mean estimator fails catastrophically. We also consider a cosmological application, where our approach leads to $\sim$ 3 to 6 times more samples than current state-of-the-art techniques in 1/3 of the time. In all cases our learnt harmonic mean estimator is shown to be highly accurate. The estimator is computationally scalable and can be applied to problems of dimension $O(10^3)$ and beyond. Code implementing the learnt harmonic mean estimator is made publicly available
Deciphering and integrating invariants for neural operator learning with various physical mechanisms
Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation (PDE) solvers. However, most existing operator learning methods assume that the data originate from a single physical mechanism, limiting their applicability and performance in more realistic scenarios. To this end, we propose Physical Invariant Attention Neural Operator (PIANO) to decipher and integrate the physical invariants (PI) for operator learning from the PDE series with various physical mechanisms. PIANO employs self-supervised learning to extract physical knowledge and attention mechanisms to integrate them into dynamic convolutional layers. Compared to existing techniques, PIANO can reduce the relative error by 13.6\%-82.2\% on PDE forecasting tasks across varying coefficients, forces, or boundary conditions. Additionally, varied downstream tasks reveal that the PI embeddings deciphered by PIANO align well with the underlying invariants in the PDE systems, verifying the physical significance of PIANO. The source code will be publicly available at: //github.com/optray/PIANO.
Improving the resolution of fluorescence microscopy beyond the diffraction limit can be achievedby acquiring and processing multiple images of the sample under different illumination conditions.One of the simplest techniques, Random Illumination Microscopy (RIM), forms the super-resolvedimage from the variance of images obtained with random speckled illuminations. However, thevalidity of this process has not been fully theorized. In this work, we characterize mathematicallythe sample information contained in the variance of diffraction-limited speckled images as a functionof the statistical properties of the illuminations. We show that an unambiguous two-fold resolutiongain is obtained when the speckle correlation length coincides with the width of the observationpoint spread function. Last, we analyze the difference between the variance-based techniques usingrandom speckled illuminations (as in RIM) and those obtained using random fluorophore activation(as in Super-resolution Optical Fluctuation Imaging, SOFI).
Model averaging has received much attention in the past two decades, which integrates available information by averaging over potential models. Although various model averaging methods have been developed, there are few literatures on the theoretical properties of model averaging from the perspective of stability, and the majority of these methods constrain model weights to a simplex. The aim of this paper is to introduce stability from statistical learning theory into model averaging. Thus, we define the stability, asymptotic empirical risk minimizer, generalization, and consistency of model averaging and study the relationship among them. Our results indicate that stability can ensure that model averaging has good generalization performance and consistency under reasonable conditions, where consistency means model averaging estimator can asymptotically minimize the mean squared prediction error. We also propose a L2-penalty model averaging method without limiting model weights and prove that it has stability and consistency. In order to reduce the impact of tuning parameter selection, we use 10-fold cross-validation to select a candidate set of tuning parameters and perform a weighted average of the estimators of model weights based on estimation errors. The Monte Carlo simulation and an illustrative application demonstrate the usefulness of the proposed method.
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