Non-Adaptive Policies for 20 Questions Target Localization

The problem of target localization with noise is addressed. The target is a sample from a continuous random variable with known distribution and the goal is to locate it with minimum mean squared error distortion. The localization scheme or policy proceeds by queries, or questions, weather or not the target belongs to some subset as it is addressed in the 20-question framework. These subsets are not constrained to be intervals and the answers to the queries are noisy. While this situation is well studied for adaptive querying, this paper is focused on the non adaptive querying policies based on dyadic questions. The asymptotic minimum achievable distortion under such policies is derived. Furthermore, a policy named the Aurelian1 is exhibited which achieves asymptotically this distortion

COARSE-TO-FINE MULTIPLE TESTING STRATEGIES.

We consider a multiple testing scenario encountered in the biological sciences and elsewhere: there are a great many null hypotheses about the distribution of a high-dimensional random variable but only a very small fraction are false (or “active”); moreover, controlling the false positives rate through FWER or FDR is imperative. Not surprisingly, the usual methods applied to control the two former criteria are often too conservative and lead to a small number of true detections. Clearly, some additional assumptions or domain-specific knowledge are then necessary to improve power. Motivated by applications in genomics, particularly genome-wide association studies, we suppose the set indexing the hypotheses has a natural hierarchical structure, the simplest case being a partition into “cells.” In principle, it should then be possible to gain power if the active hypotheses tend to cluster within cells. We explore different coarse-to-fine, two-level multiple testing strategies, which control the FWER or the FDR and are designed to gain power relative to usual single level methods, in so far as clustering allows it. Simulations confirm a sharp improvement for in data models we consider

Learning High-Dimensional Nonparametric Differential Equations via Multivariate Occupation Kernel Functions

Learning a nonparametric system of ordinary differential equations (ODEs) from $n$ trajectory snapshots in a $d$-dimensional state space requires learning $d$ functions of $d$ variables. Explicit formulations scale quadratically in $d$ unless additional knowledge about system properties, such as sparsity and symmetries, is available. In this work, we propose a linear approach to learning using the implicit formulation provided by vector-valued Reproducing Kernel Hilbert Spaces. By rewriting the ODEs in a weaker integral form, which we subsequently minimize, we derive our learning algorithm. The minimization problem's solution for the vector field relies on multivariate occupation kernel functions associated with the solution trajectories. We validate our approach through experiments on highly nonlinear simulated and real data, where $d$ may exceed 100. We further demonstrate the versatility of the proposed method by learning a nonparametric first order quasilinear partial differential equation.Comment: 22 pages, 3 figures, submitted to Neurips 202

Learning nonparametric ordinary differential equations from noisy data

Learning nonparametric systems of Ordinary Differential Equations (ODEs) dot x = f(t,x) from noisy data is an emerging machine learning topic. We use the well-developed theory of Reproducing Kernel Hilbert Spaces (RKHS) to define candidates for f for which the solution of the ODE exists and is unique. Learning f consists of solving a constrained optimization problem in an RKHS. We propose a penalty method that iteratively uses the Representer theorem and Euler approximations to provide a numerical solution. We prove a generalization bound for the L2 distance between x and its estimator and provide experimental comparisons with the state-of-the-art.Comment: 25 pages, 6 figure

Synthesis, characterization, and investigation of the antioxidant activity of some 1,2,4-benzothiadiazine-1,1-dioxides bearing sulfonylthioureas moieties

peer reviewedA series of 1,2,4-benzothiadiazine-1,1-dioxides bearing a sulfonylthiourea moiety were synthesized, characterized, and screened for their antioxidant activity, using six antioxidant analytical assays comparatively to reference compounds, ascorbic acid and quercetin. The results indicated that several compounds demonstrated strong antioxidant activity in DPPH, ABTS, H2O2, and lipid peroxidation assays where some of them were either as active as or more active than reference compounds. However, all compounds were largely less active than references compounds in the reducing power assay. The results indicated that the thiourea moiety probably played a crucial role in the antioxidant activity of the target compounds, as a thiolate ion. The most favorable R1 groups were the hydrogen atom and methyl group, followed by phenyl and benzyl groups, whereas the most favorable R2 group was iPr, followed by the phenyl and methyl groups. The combination of benzothiadiazine ring with sulfonylthiourea moieties led to valuable new antioxidants, which could be used in the treatment or the prevention of certain diseases or in the field of cosmetics, which needs further investigations in the future

Learning Nonparametric Ordinary Differential Equations: Application to Sparse and Noisy Data

Learning nonparametric systems of Ordinary Differential Equations (ODEs) x˙=f(t,x) from noisy and sparse data is an emerging machine learning topic. We use the well-developed theory of Reproducing Kernel Hilbert Spaces (RKHS) to define candidates for f for which the solution of the ODE exists and is unique. Learning f consists of solving a constrained optimization problem in an RKHS. We propose a penalty method that iteratively uses the Representer theorem and Euler approximations to provide a numerical solution. We prove a generalization bound for the L2 distance between x and its estimator. Experiments are provided for the FitzHugh Nagumo oscillator and for the prediction of the Amyloid level in the cortex of aging subjects. In both cases, we show competitive results when compared with the state of the art

Figure S9 from The Origin of Highly Elevated Cell-Free DNA in Healthy Individuals and Patients with Pancreatic, Colorectal, Lung, or Ovarian Cancer

Supplemental Figure 9. Plasma AST and ALT levels before and ~24 hours after surgery for pancreatic cancer. AST and ALT levels substantially increased in all five patients.</p