Theoretical analysis of cross-validation for estimating the risk of the k-Nearest Neighbor classifier

The present work aims at deriving theoretical guaranties on the behavior of some cross-validation procedures applied to the $k$-nearest neighbors ($k$NN) rule in the context of binary classification. Here we focus on the leave-$p$-out cross-validation (L$p$O) used to assess the performance of the $k$NN classifier. Remarkably this L$p$O estimator can be efficiently computed in this context using closed-form formulas derived by \cite{CelisseMaryHuard11}. We describe a general strategy to derive moment and exponential concentration inequalities for the L$p$O estimator applied to the $k$NN classifier. Such results are obtained first by exploiting the connection between the L$p$O estimator and U-statistics, and second by making an intensive use of the generalized Efron-Stein inequality applied to the L$1$O estimator. One other important contribution is made by deriving new quantifications of the discrepancy between the L$p$O estimator and the classification error/risk of the $k$NN classifier. The optimality of these bounds is discussed by means of several lower bounds as well as simulation experiments

Synthesis of the Cyclohepta[<i>e</i>]hydrindane Core of the Marine Homoverrucosane Diterpenoid Gagunin E

The synthesis of the A–B-<i>cis</i> B–C-<i>trans</i> annulated cyclohepta­[<i>e</i>]­hydrindane core of gagunin E with a fully elaborated B–C ring segment has been achieved. Using an adaptable A ring building block, the B ring was annulated by (4 + 2)-cycloaddition and the C ring by ring-closing metathesis. The angular methyl groups were attached by electrophilic cyclopropanation–ring opening

Synthesis of the Cyclohepta[<i>e</i>]hydrindane Core of the Marine Homoverrucosane Diterpenoid Gagunin E

The synthesis of the A–B-<i>cis</i> B–C-<i>trans</i> annulated cyclohepta­[<i>e</i>]­hydrindane core of gagunin E with a fully elaborated B–C ring segment has been achieved. Using an adaptable A ring building block, the B ring was annulated by (4 + 2)-cycloaddition and the C ring by ring-closing metathesis. The angular methyl groups were attached by electrophilic cyclopropanation–ring opening

{1,6}-Transannular Catalytic Asymmetric Gosteli–Claisen Rearrangement

The first uncatalyzed and [Cu(R-box)L₂](SbF₆)₂-catalyzed {1,6}-transannular Gosteli–Claisen rearrangement of cyclic 2-alkoxycarbonyl-substituted allyl vinyl ethers to afford medium- and large-sized carbacycles is disclosed

Synthesis of the Cyclohepta[<i>e</i>]hydrindane Core of the Marine Homoverrucosane Diterpenoid Gagunin E

The synthesis of the A–B-<i>cis</i> B–C-<i>trans</i> annulated cyclohepta­[<i>e</i>]­hydrindane core of gagunin E with a fully elaborated B–C ring segment has been achieved. Using an adaptable A ring building block, the B ring was annulated by (4 + 2)-cycloaddition and the C ring by ring-closing metathesis. The angular methyl groups were attached by electrophilic cyclopropanation–ring opening

Total Synthesis and Structural Assignment of Curvicollide C

The first total synthesis of (+)-curvicollide C has been accomplished. Cross-metathesis and Julia–Kocienski olefination were instrumental in the synthesis of 1,3-diene segments and allowed for a ternary-convergent synthetic design. A full structural assignment is proposed for (−)-curvicollide C, a uniquely structured polyketide of fungal origin

Total Synthesis and Structural Assignment of Curvicollide C

The first total synthesis of (+)-curvicollide C has been accomplished. Cross-metathesis and Julia–Kocienski olefination were instrumental in the synthesis of 1,3-diene segments and allowed for a ternary-convergent synthetic design. A full structural assignment is proposed for (−)-curvicollide C, a uniquely structured polyketide of fungal origin

Total Synthesis and Structural Assignment of Curvicollide C

The first total synthesis of (+)-curvicollide C has been accomplished. Cross-metathesis and Julia–Kocienski olefination were instrumental in the synthesis of 1,3-diene segments and allowed for a ternary-convergent synthetic design. A full structural assignment is proposed for (−)-curvicollide C, a uniquely structured polyketide of fungal origin

Progress toward the Total Synthesis of Gukulenin A: Photochemically Triggered Two-Carbon Ring Expansion Key to α‑Tropolonic Ether Synthesis

The ex-chiral-pool synthesis of an advanced gukulenin A precursor from (−)-piperitone is revealed. Key C/C connecting maneuvers to the synthesis of a C₂ dissymmetric bis­(α-tropolonic) ether building block are a ring-contracting Meinwald rearrangement, a photochemically triggered two-carbon ring expansion, and a homodimerization by cross-metathesis

Cyclopentanoids by Uncatalyzed Intramolecular Carbonyl Ene (ICE) Reaction of α‑Keto Esters

The uncatalyzed intramolecular carbonyl ene (ICE) reaction of substituted ε,ζ-unsaturated α-keto esters to terpenoid-related building blocks has been studied. We found a beneficial effect of a silyl substituent at the ene segment on the kinetics of the ICE reaction. A generalizable and scalable synthesis of ε,ζ-unsaturated α-keto esters from allylic alcohols was developed