Efficient First Order Methods for Linear Composite Regularizers

A wide class of regularization problems in machine learning and statistics employ a regularization term which is obtained by composing a simple convex function \omega with a linear transformation. This setting includes Group Lasso methods, the Fused Lasso and other total variation methods, multi-task learning methods and many more. In this paper, we present a general approach for computing the proximity operator of this class of regularizers, under the assumption that the proximity operator of the function \omega is known in advance. Our approach builds on a recent line of research on optimal first order optimization methods and uses fixed point iterations for numerically computing the proximity operator. It is more general than current approaches and, as we show with numerical simulations, computationally more efficient than available first order methods which do not achieve the optimal rate. In particular, our method outperforms state of the art O(1/T) methods for overlapping Group Lasso and matches optimal O(1/T^2) methods for the Fused Lasso and tree structured Group Lasso.Comment: 19 pages, 8 figure

Sphingolipid metabolism products: potential new players in the pathogenesis of bortezomib-induced neuropathic pain

Chemotherapy-induced peripheral neurotoxicity (CIPN) is one of the major dose-limiting adverse events of widely used drugs in both the oncologic and hematologic setting (1). Among its cardinal symptoms, neuropathic pain is frequently present (2). In particular, the incidence of bortezomib-induced peripheral neurotoxicity (BIPN) and neuropathic pain ranges from 14–45% and 5–39%, respectively, in myeloma multiple patients. BIPN is more frequently developed in pretreated patients, compared to those being chemotherapy-naïve (3,4), and this difference mostly accounts for the wide variability in the observed incidence rates. Bortezomib is the first proteasome inhibitor introduced in clinical practice. The mechanisms underlying the pathogenesis of peripheral neurotoxicity in bortezomib- treated patients are, yet, not fully elucidated (3,4)

Inconclusive evidence to support the use of minimally-invasive radiofrequency denervation against chronic low back pain

Low back pain (LBP), defined as the localized pain or discomfort between the costal margins and superior gluteal line, with or without associated lower limb pain, is one of the most commonly encountered pain syndromes in adults. It is considered chronic LBP (CLBP), when pain persists for more than three months (1). CLBP might be disabling with increased missing hours of productive work or of personal activities and it can also be associated with significant excess of healthcare costs (2). Commonly, CLBP also gives rise to the genesis or exacerbation of various psychiatric disorders, such as depression and/or anxiety (3)

On Sparsity Inducing Regularization Methods for Machine Learning

During the past years there has been an explosion of interest in learning methods based on sparsity regularization. In this paper, we discuss a general class of such methods, in which the regularizer can be expressed as the composition of a convex function $\omega$ with a linear function. This setting includes several methods such the group Lasso, the Fused Lasso, multi-task learning and many more. We present a general approach for solving regularization problems of this kind, under the assumption that the proximity operator of the function $\omega$ is available. Furthermore, we comment on the application of this approach to support vector machines, a technique pioneered by the groundbreaking work of Vladimir Vapnik.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1104.143

Predictive Biomarkers of Oxaliplatin-Induced Peripheral Neurotoxicity

Oxaliplatin (OXA) is a platinum compound primarily used in the treatment of gastrointestinal cancer. OXA-induced peripheral neurotoxicity (OXAIPN) is the major non-hematological dose-limiting toxicity of OXA-based chemotherapy and includes acute transient neurotoxic effects that appear soon after OXA infusion, and chronic non-length dependent sensory neuronopathy symmetrically affecting both upper and lower limbs in a stocking-and-glove distribution. No effective strategy has been established to reverse or treat OXAIPN. Thus, it is necessary to early predict the occurrence of OXAIPN during treatment and possibly modify the OXA-based regimen in patients at high risk as an early diagnosis and intervention may slow down neuropathy progression. However, identifying which patients are more likely to develop OXAIPN is clinically challenging. Several objective and measurable early biomarkers for OXAIPN prediction have been described in recent years, becoming useful for informing clinical decisions about treatment. The purpose of this review is to critically review data on currently available or promising predictors of OXAIPN. Neurological monitoring, according to predictive factors for increased risk of OXAIPN, would allow clinicians to personalize treatment, by monitoring at-risk patients more closely and guide clinicians towards better counseling of patients about neurotoxicity effects of OXA

Dictionary Learning and Tensor Decomposition via the Sum-of-Squares Method

We give a new approach to the dictionary learning (also known as "sparse coding") problem of recovering an unknown $n\times m$ matrix $A$ (for $m \geq n$) from examples of the form $$y = Ax + e,$$ where $x$ is a random vector in $\mathbb R^m$ with at most $\tau m$ nonzero coordinates, and $e$ is a random noise vector in $\mathbb R^n$ with bounded magnitude. For the case $m=O(n)$, our algorithm recovers every column of $A$ within arbitrarily good constant accuracy in time $m^{O(\log m/\log(\tau^{-1}))}$, in particular achieving polynomial time if $\tau = m^{-\delta}$ for any $\delta>0$, and time $m^{O(\log m)}$ if $\tau$ is (a sufficiently small) constant. Prior algorithms with comparable assumptions on the distribution required the vector $x$ to be much sparser---at most $\sqrt{n}$ nonzero coordinates---and there were intrinsic barriers preventing these algorithms from applying for denser $x$. We achieve this by designing an algorithm for noisy tensor decomposition that can recover, under quite general conditions, an approximate rank-one decomposition of a tensor $T$, given access to a tensor $T'$ that is $\tau$-close to $T$ in the spectral norm (when considered as a matrix). To our knowledge, this is the first algorithm for tensor decomposition that works in the constant spectral-norm noise regime, where there is no guarantee that the local optima of $T$ and $T'$ have similar structures. Our algorithm is based on a novel approach to using and analyzing the Sum of Squares semidefinite programming hierarchy (Parrilo 2000, Lasserre 2001), and it can be viewed as an indication of the utility of this very general and powerful tool for unsupervised learning problems

Efficient First Order Methods for Linear Composite Regularizers

A wide class of regularization problems in machine learning and statistics employ a regularization term which is obtained by composing a simple convex function omega with a linear transformation. This setting includes Group Lasso methods, the Fused Lasso and other total variation methods, multi-task learning methods and many more. In this paper, we present a general approach for computing the proximity operator of this class of regularizers, under the assumption that the proximity operator of the function \omega is known in advance. Our approach builds on a recent line of research on optimal first order optimization methods and uses fixed point iterations for numerically computing the proximity operator. It is more general than current approaches and, as we show with numerical simulations, computationally more efficient than available first order methods which do not achieve the optimal rate. In particular, our method outperforms state of the art O(1/T) methods for overlapping Group Lasso and matches optimal O(1/T2) methods for the Fused Lasso and tree structured Group Lasso

Approximate Near Neighbors for General Symmetric Norms

We show that every symmetric normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation. Specifically, for every $n$, $d = n^{o(1)}$, and every $d$-dimensional symmetric norm $\|\cdot\|$, there exists a data structure for $\mathrm{poly}(\log \log n)$-approximate nearest neighbor search over $\|\cdot\|$ for $n$-point datasets achieving $n^{o(1)}$ query time and $n^{1+o(1)}$ space. The main technical ingredient of the algorithm is a low-distortion embedding of a symmetric norm into a low-dimensional iterated product of top-$k$ norms. We also show that our techniques cannot be extended to general norms.Comment: 27 pages, 1 figur

Perilesional edema in brain metastases as predictive factor of response to systemic therapy in non-small cell lung cancer patients: a preliminary study

Background: The significance of upfront systemic therapies as an alternative to whole brain radiotherapy (WBRT) for multiple brain metastases (BM) is debatable. Our purpose is to investigate if peritumoral edema could predict the intracranial response to systemic chemotherapy (chemo) in patients with advanced non-squamous non-small cell lung cancer (non-SQ-NSCLC) and synchronous multiple BM. Methods: In this observational cohort study, we evaluated the outcome of 28 patients with multiple BM (≥3) treated with chemo based on cisplatin/carboplatin plus pemetrexed (chemo, group A, n=17) or WBRT plus subsequent chemo (group B, n=11). The intracranial response, assessed by the response assessment neuro-oncology (RANO) BM criteria, was correlated with the degree of BM-associated edema estimated by the maximum diameter ratio among fluid attenuated inversion recovery (FLAIR) and gadolinium-enhanced T1WI (T1Gd) per each BM at the baseline brain magnetic resonance imaging (MRI). Results: No differences were observed in baseline characteristics between both groups, except for the number of patients under steroid treatment that was clearly superior in group B (P=0.007). Median OS was similar between groups. Regarding FLAIR/T1Gd ratio (F/Gd), patients treated with chemo alone exhibited significantly higher values (P=0.001) in those who developed intracranial progression disease (PD) (2.80±0.32 mm), compared with those who achieved partial response (PR) (1.30±0.11 mm) or stable disease (SD) (1.35±0.09 mm). In patients treated with WBRT, F/Gd ratio was not predictive of response. Conclusions: Peritumoral edema estimated by F/Gd ratio appears a promising predictive tool to identify oligosymptomatic patients with multiple BM in whom WBRT can be postponed