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Found 8 papers, 0 papers with code
On Rate-Optimal Partitioning Classification from Observable and from Privatised Data
Here, we study the problem under much milder assumptions: in addition to the standard Lipschitz and margin conditions, a novel characteristic of the absolutely continuous component is introduced, by which the exact convergence rate of the classification error probability is calculated, both for the binary and for the multi-label cases.
Lossless Transformations and Excess Risk Bounds in Statistical Inference
After characterizing lossless transformations, i. e., transformations for which the excess risk is zero for all loss functions, we construct a partitioning test statistic for the hypothesis that a given transformation is lossless and show that for i. i. d.
Repeated Observations for Classification
We study the problem nonparametric classification with repeated observations.
On the strong stability of ergodic iterations
We revisit processes generated by iterated random functions driven by a stationary and ergodic sequence.
Tree density estimation
data we identify an optimal tree $T^*$ and efficiently construct a tree density estimate $f_n$ such that, without any regularity conditions on the density $f$, one has $\lim_{n\to \infty} \int |f_n(\boldsymbol x)-f_{T^*}(\boldsymbol x)|d\boldsymbol x=0$ a. s. For Lipschitz $f$ with bounded support, $\mathbb E \left\{ \int |f_n(\boldsymbol x)-f_{T^*}(\boldsymbol x)|d\boldsymbol x\right\}=O\big(n^{-1/4}\big)$, a dimension-free rate.
On the consistency of the Kozachenko-Leonenko entropy estimate
We revisit the problem of the estimation of the differential entropy $H(f)$ of a random vector $X$ in $R^d$ with density $f$, assuming that $H(f)$ exists and is finite.
Statistics Theory Statistics Theory
Strongly universally consistent nonparametric regression and classification with privatised data
In this paper we revisit the classical problem of nonparametric regression, but impose local differential privacy constraints.
Universal consistency and rates of convergence of multiclass prototype algorithms in metric spaces
We first obtain rates for the standard $k$-NN rule under a margin condition and a new generalized-Lipschitz condition.
