Estimating a potential without the agony of the partition function

Estimating a Gibbs density function given a sample is an important problem in computational statistics and statistical learning. Although the well established maximum likelihood method is commonly used, it requires the computation of the partition function (i.e., the normalization of the density). This function can be easily calculated for simple low-dimensional problems but its computation is difficult or even intractable for general densities and high-dimensional problems. In this paper we propose an alternative approach based on Maximum A-Posteriori (MAP) estimators, we name Maximum Recovery MAP (MR-MAP), to derive estimators that do not require the computation of the partition function, and reformulate the problem as an optimization problem. We further propose a least-action type potential that allows us to quickly solve the optimization problem as a feed-forward hyperbolic neural network. We demonstrate the effectiveness of our methods on some standard data sets

DRIP: Deep Regularizers for Inverse Problems

In this paper we consider inverse problems that are mathematically ill-posed. That is, given some (noisy) data, there is more than one solution that approximately fits the data. In recent years, deep neural techniques that find the most appropriate solution, in the sense that it contains a-priori information, were developed. However, they suffer from several shortcomings. First, most techniques cannot guarantee that the solution fits the data at inference. Second, while the derivation of the techniques is inspired by the existence of a valid scalar regularization function, such techniques do not in practice rely on such a function, and therefore veer away from classical variational techniques. In this work we introduce a new family of neural regularizers for the solution of inverse problems. These regularizers are based on a variational formulation and are guaranteed to fit the data. We demonstrate their use on a number of highly ill-posed problems, from image deblurring to limited angle tomography

pathGCN: Learning General Graph Spatial Operators from Paths

Graph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations - spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined spatial operator based on the graph Laplacian is often chosen, allowing only the point-wise operations to be learnt. However, learning a meaningful spatial operator is critical for developing more expressive GCNs for improved performance. In this paper we propose pathGCN, a novel approach to learn the spatial operator from random paths on the graph. We analyze the convergence of our method and its difference from existing GCNs. Furthermore, we discuss several options of combining our learnt spatial operator with point-wise convolutions. Our extensive experiments on numerous datasets suggest that by properly learning both the spatial and point-wise convolutions, phenomena like over-smoothing can be inherently avoided, and new state-of-the-art performance is achieved.Comment: ICML 202

Preclinical to clinical development of the novel camptothecin nanopharmaceutical CRLX101

AbstractCamptothecin (CPT) is a potent broad-spectrum anticancer agent that acts through inhibition of topoisomerase 1. Clinical development of CPT was unsuccessful due to poor drug solubility, insufficient in vivo stability of the active form, and toxicity. In order to address these issues, a polymeric nanoparticle comprised of cyclodextrin-poly(ethylene glycol) copolymer (CDP) conjugated to CPT (CRLX101) has been developed and Phase 2 clinical studies are ongoing. Camptothecin is conjugated to the polymer in its active form at 10–12wt.% loading. CRLX101 self-assembles in solution into nanoparticles with an apparent solubility increase of >1000-fold as compared to the parent drug camptothecin. Preclinical studies exhibited CRLX101 pharmacokinetics superior to the parent drug. Drug concentration in tumor relative to plasma and other major organs is consistent with the enhanced permeation and retention (EPR) anticipated from a nanoparticle. Significant anti-tumor activity was observed that is superior when compared to irinotecan across a broad range of xenograft models. Pharmacokinetic data are consistent with the prolonged half-life and increased AUC. The CRLX101 preclinical and clinical data confirm that CDP can address not only solubility, formulation, toxicity, and pharmacokinetic challenges associated with administration of CPT, but more importantly, can impart unique biological properties, that enhance pharmacodynamics and efficacy of camptothecin

Efficient Subgraph GNNs by Learning Effective Selection Policies

Subgraph GNNs are provably expressive neural architectures that learn graph representations from sets of subgraphs. Unfortunately, their applicability is hampered by the computational complexity associated with performing message passing on many subgraphs. In this paper, we consider the problem of learning to select a small subset of the large set of possible subgraphs in a data-driven fashion. We first motivate the problem by proving that there are families of WL-indistinguishable graphs for which there exist efficient subgraph selection policies: small subsets of subgraphs that can already identify all the graphs within the family. We then propose a new approach, called Policy-Learn, that learns how to select subgraphs in an iterative manner. We prove that, unlike popular random policies and prior work addressing the same problem, our architecture is able to learn the efficient policies mentioned above. Our experimental results demonstrate that Policy-Learn outperforms existing baselines across a wide range of datasets.Comment: 21 pages, 3 figure

CRLX101 (formerly IT-101)–A Novel Nanopharmaceutical of Camptothecin in Clinical Development

CRLX101 (formerly IT-101) is a first-in-class nanopharmaceutical, currently in Phase 2a development, which has been developed by covalently conjugating camptothecin (CPT) to a linear, cyclodextrin-polyethylene glycol (CD-PEG) co-polymer that self-assembles into nanoparticles. As a nanometer-scale drug carrier system, the cyclodextrin polymeric nanoparticle technology, referred to as “CDP”, has unique design features and capabilities. Specifically, CRLX101 preclinical and clinical data confirm that CDP can address not only solubility, formulation, toxicity, and pharmacokinetic challenges associated with administration of CPT, but more importantly, can impart unique biological properties that enhance CPT pharmacodynamics and efficacy

Quantized Convolutional Neural Networks Through the Lens of Partial Differential Equations

Quantization of Convolutional Neural Networks (CNNs) is a common approach to ease the computational burden involved in the deployment of CNNs, especially on low-resource edge devices. However, fixed-point arithmetic is not natural to the type of computations involved in neural networks. In this work, we explore ways to improve quantized CNNs using PDE-based perspective and analysis. First, we harness the total variation (TV) approach to apply edge-aware smoothing to the feature maps throughout the network. This aims to reduce outliers in the distribution of values and promote piece-wise constant maps, which are more suitable for quantization. Secondly, we consider symmetric and stable variants of common CNNs for image classification, and Graph Convolutional Networks (GCNs) for graph node-classification. We demonstrate through several experiments that the property of forward stability preserves the action of a network under different quantization rates. As a result, stable quantized networks behave similarly to their non-quantized counterparts even though they rely on fewer parameters. We also find that at times, stability even aids in improving accuracy. These properties are of particular interest for sensitive, resource-constrained, low-power or real-time applications like autonomous driving