Adaptive Regularization Algorithms with Inexact Evaluations for Nonconvex Optimization

A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that is constraints whose evaluation and enforcement has negligible cost) under the assumption that the derivative of highest degree is $\beta$-H\"{o}lder continuous. It features a very flexible adaptive mechanism for determining the inexactness which is allowed, at each iteration, when computing objective function values and derivatives. The complexity analysis covers arbitrary optimality order and arbitrary degree of available approximate derivatives. It extends results of Cartis, Gould and Toint (2018) on the evaluation complexity to the inexact case: if a $q$th order minimizer is sought using approximations to the first $p$ derivatives, it is proved that a suitable approximate minimizer within $\epsilon$ is computed by the proposed algorithm in at most $O(\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ iterations and at most $O(|\log(\epsilon)|\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ approximate evaluations. An algorithmic variant, although more rigid in practice, can be proved to find such an approximate minimizer in $O(|\log(\epsilon)|+\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ evaluations.While the proposed framework remains so far conceptual for high degrees and orders, it is shown to yield simple and computationally realistic inexact methods when specialized to the unconstrained and bound-constrained first- and second-order cases. The deterministic complexity results are finally extended to the stochastic context, yielding adaptive sample-size rules for subsampling methods typical of machine learning.Comment: 32 page

Adaptive Regularization for Nonconvex Optimization Using Inexact Function Values and Randomly Perturbed Derivatives

A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function with Lipschitz continuous $p$-th derivative and given an arbitrary optimality order $q \leq p$, it is shown that this algorithm will, in expectation, compute such a point in at most $O\left(\left(\min_{j\in\{1,\ldots,q\}}\epsilon_j\right)^{-\frac{p+1}{p-q+1}}\right)$ inexact evaluations of $f$ and its derivatives whenever $q\in\{1,2\}$, where $\epsilon_j$ is the tolerance for $j$th order accuracy. This bound becomes at most $O\left(\left(\min_{j\in\{1,\ldots,q\}}\epsilon_j\right)^{-\frac{q(p+1)}{p}}\right)$ inexact evaluations if $q>2$ and all derivatives are Lipschitz continuous. Moreover these bounds are sharp in the order of the accuracy tolerances. An extension to convexly constrained problems is also outlined.Comment: 22 page

Is oral metronomic cyclophosphamide (CTX) an effective palliative treatment for patients with metastatic breast carcinoma (ABC)? experience from a retrospective series of patients

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TTF-1/p63-positive poorly differentiated NSCLC: A histogenetic hypothesis from the basal reserve cell of the terminal respiratory unit

TTF-1 is expressed in the alveolar epithelium and in the basal cells of distal terminal bronchioles. It is considered the most sensitive and specific marker to define the adenocarcinoma arising from the terminal respiratory unit (TRU). TTF-1, CK7, CK5/6, p63 and p40 are useful for typifying the majority of non-small-cell lung cancers, with TTF and CK7 being typically expressed in adenocarcinomas and the latter three being expressed in squamous cell carcinoma. As tumors with coexpression of both TTF-1 and p63 in the same cells are rare, we describe different cases that coexpress them, suggesting a histogenetic hypothesis of their origin. We report 10 cases of poorly differentiated non-small-cell lung carcinoma (PD-NSCLC). Immunohistochemistry was performed by using TTF-1, p63, p40 (∆Np63), CK5/6 and CK7. EGFR and BRAF gene mutational analysis was performed by using real-time PCR. All the cases showed coexpression of p63 and TTF-1. Six of them showing CK7+ and CK5/6− immunostaining were diagnosed as “TTF-1+ p63+ adenocarcinoma”. The other cases of PD-NSCLC, despite the positivity for CK5/6, were diagnosed as “adenocarcinoma, solid variant”, in keeping with the presence of TTF-1 expression and p40 negativity. A “wild type” genotype of EGFR was evidenced in all cases. TTF1 stained positively the alveolar epithelium and the basal reserve cells of TRU, with the latter also being positive for p63. The coexpression of p63 and TTF-1 could suggest the origin from the basal reserve cells of TRU and represent the capability to differentiate towards different histogenetic lines. More aggressive clinical and morphological features could characterize these “basal-type tumors” like those in the better known “basal-like” cancer of the breast

Underwater archaeological mosaicing

Archaeological mosaicing is one of the challenges of the computer vision community and it can be faced in a 2D or 3D approach. This contribution regards a methodology to do a mosaic of an underwater bi-dimensional scene. A number of problems arise from the acquisition of images by a remote operated vehicle. Radial distortion, poor luminosity, cloud water, presence of artefacts are part of the issues that can occur; for instance, the radial distortion has been corrected to improve the quality of the input images. Keypoints detection (through SIFT transform), Singular Value Decomposition, Random Samples Consensus are some of the techniques applied in our method. This contribution regards the mosaicing of seabed landscapes, in order to represent higher resolution photos of whole sites with wrecks in a fast and safe fashion. A stereo vision system has been arranged by adding two cameras to the payload aboard a Remotely Operated Vehicle. A number of problems arise due to poor luminosity, cloudy water, water distortion and presence of artifacts. A robust algorithm has been de¯ned to reduce the radial distortion of the camera lenses and to enhance the results

Usefulness of regional right ventricular and right atrial strain for prediction of early and late right ventricular failure following a left ventricular assist device implant: A machine learning approach

Background: Identifying candidates for left ventricular assist device surgery at risk of right ventricular failure remains difficult. The aim was to identify the most accurate predictors of right ventricular failure among clinical, biological, and imaging markers, assessed by agreement of different supervised machine learning algorithms. Methods: Seventy-four patients, referred to HeartWare left ventricular assist device since 2010 in two Italian centers, were recruited. Biomarkers, right ventricular standard, and strain echocardiography, as well as cath-lab measures, were compared among patients who did not develop right ventricular failure (N = 56), those with acute–right ventricular failure (N = 8, 11%) or chronic–right ventricular failure (N = 10, 14%). Logistic regression, penalized logistic regression, linear support vector machines, and naïve Bayes algorithms with leave-one-out validation were used to evaluate the efficiency of any combination of three collected variables in an “all-subsets” approach. Results: Michigan risk score combined with central venous pressure assessed invasively and apical longitudinal systolic strain of the right ventricular–free wall were the most significant predictors of acute–right ventricular failure (maximum receiver operating characteristic–area under the curve = 0.95, 95% confidence interval = 0.91–1.00, by the naïve Bayes), while the right ventricular–free wall systolic strain of the middle segment, right atrial strain (QRS-synced), and tricuspid annular plane systolic excursion were the most significant predictors of Chronic-RVF (receiver operating characteristic–area under the curve = 0.97, 95% confidence interval = 0.91–1.00, according to naïve Bayes). Conclusion: Apical right ventricular strain as well as right atrial strain provides complementary information, both critical to predict acute–right ventricular failure and chronic–right ventricular failure, respectively