44 problems

Tightness conjecture for the quantum-to-classical privacy conversion bound
arXiv@arxiv
Let $n$ be the number of inputs and $\rho_x$ range over quantum locally differentially private mechanisms. Define $\varepsilon_{\inf}=\varepsilon_{\inf}(n,\varepsilon)$ as the infi…
Conjectureopendifferential-privacy privacy-conversion quantum-information
0
The small-noise quadratic privacy-subsidy conjecture
arXiv@arxiv
For an $b5$ -differentially private channel with Laplace noise, let $c3_\varepsilon$ denote the noise scale and let the privacy-subsidy rate be the subsidy generated by the resultin…
Conjectureopendifferential-privacy market-microstructure stochastic-processes
0
Local-limit-theorem justification for Gaussian approximations in privatized-data sampling
arXiv@arxiv
Local-limit-theorem conjecture. Using a local limit theorem, along with an adaptation of the paper's analyses, could potentially give theoretical support to the procedure of Bernst…
Conjectureopenasymptotic-approximations differential-privacy local-limit-theorems
0
Unavoidability of the logarithmic adaptivity cost in differentially private estimation
arXiv@arxiv
The covariance matrix … , but its privacy term incurs a logarithmic-factor loss. Unavoidability conjecture. This logarithmic loss is unavoidable for adaptive estimation under diffe…
Conjectureopenadaptive-estimation covariance-estimation differential-privacy
0
The computational gap conjecture for higher-order network parameter estimation
arXiv@arxiv
Computational gap conjecture. When the MLE fails to exist, there is an intrinsic gap between the information-theoretic lower bound on estimation risk and the performance achievable…
Conjectureopendifferential-privacy higher-order-networks statistical-computation
1
Geng et al.'s staircase optimality conjecture for vector queries
arXiv@arxiv
Let $q$ be a query with $\\|\cdot\\|_1$ -sensitivity $\Delta$ , and consider additive $\varepsilon$ -differentially private mechanisms of the form $M(D)=q(D)+X$ , where $X$ is an…
Conjectureopendifferential-privacy optimization staircase-mechanisms
0
Two-block-design sufficiency conjecture for optimal PUT
arXiv@arxiv
Two-block-design sufficiency conjecture. A single block design is not sufficient to attain the optimal PUT, whereas the two block designs with $k=1$ and $k=2$ are sufficient to att…
Conjectureopendifferential-privacy distribution-estimation information-theory
0
Conjecture on censoring-rate effects in private Cox regression and cumulative-hazard estimation
arXiv@arxiv
Censoring-rate conjecture. The observed difference in how censoring affects estimation error for $\beta_0$ and for $\Lambda_0(\cdot)$ is due to differences in whether the non-priva…
Conjectureopencox-regression differential-privacy survival-analysis
0
Conjecture on censoring effects in private Cox regression and cumulative-hazard estimation
arXiv@arxiv
Grid-averaging conjecture. It may be possible to relax the relevant sample-size condition by first obtaining private versions of $S^{(1)}(t,\beta_0)$ and $S^{(0)}(t,\beta_0)$ that…
Conjectureopencox-regression differential-privacy federated-learning
0
The conjecture that pruning removes redundant parameters while preserving critical network components
arXiv@arxiv
Pruning conjecture. Such pruning effectively removes redundant or less informative parameters while preserving critical components of the network.
Conjectureopendifferential-privacy model-pruning neural-networks
0
Necessity of the second bilevel complexity term in differentially private ERM
arXiv@arxiv
The setting is differentially private bilevel empirical risk minimization, where the upper-bound rates contain a principal single-level term and additional terms reflecting the bil…
Conjectureopenbilevel-optimization differential-privacy optimization
0
Conjecture on gentleness of measurements under polar decomposition
arXiv@arxiv
Gentleness conjecture. The measurement consisting of the operators $|M_y|$ has at least the same gentleness as the measurement given by the operators $M_y$ .
Conjectureopendifferential-privacy quantum-information quantum-measurements
1
The necessity of forgetting for optimal globally private bandit algorithms
arXiv@arxiv
In an $epsilon$ -global differentially private stochastic bandit, an algorithm is said to forget when it discards past rewards between independent episodes. Forgetting-necessity con…
Conjectureopendifferential-privacy multi-armed-bandits regret-minimization
1
Conjecture that the heterogeneous minimax lower bound is not tight
arXiv@arxiv
Conjecture. The lower bound in Theorem $$ is not tight.
Conjectureopendifferential-privacy functional-data-analysis minimax-theory
0
Aden-Aden-Arieli et al. sample-complexity conjecture for privately learning Gaussian mixtures
arXiv@arxiv
Aden-Aden-Arieli et al.'s sample-complexity conjecture. Only
Conjectureopendifferential-privacy gaussian-mixtures sample-complexity
0
Necessity of the logarithmic factor for instance-optimal private estimation
arXiv@arxiv
Let the data domain be a finite metric space, and consider private density estimation under Wasserstein distance with instance-optimal guarantees. Logarithmic-factor necessity conj…
Conjectureopendensity-estimation differential-privacy wasserstein-distance
0
Worse non-asymptotic upper-bound conjecture for the modified adaptive private BAI algorithm
arXiv@arxiv
Let $\adapttt{}$ be the modified adaptive algorithm for differentially private best-arm identification, and let $\delta$ denote the confidence level. Its modified transportation co…
Conjectureopenbandit-theory best-arm-identification differential-privacy
0
Arm-level distinguishability conjecture for private regret minimisation and best-arm identification
arXiv@arxiv
Consider regret minimisation and best-arm identification (BAI) under differential privacy, at an arbitrary privacy level. Let an arm-level measure of distinguishability mean a quan…
Conjectureopenbandit-theory best-arm-identification differential-privacy
0
Mean-agnostic empirical distinguishability conjecture for private best-arm identification
arXiv@arxiv
Let $W^{G,\epsilon}_{a,b}$ be the transportation cost used to measure distinguishability between arms $a$ and $b$ in the Gaussian private best-arm identification setting, and let i…
Conjectureopenbest-arm-identification differential-privacy sequential-testing
0
Non-asymptotic sample-complexity conjecture for adaptive differentially private best-arm identification
arXiv@arxiv
Let $H(\boldsymbol{\nu},\epsilon)$ denote the instance-dependent complexity appearing in the analysis of the adaptive algorithm $\adaptt{}$ , and let $\alpha>1$ be an algorithmic hy…
Conjectureopenbest-arm-identification differential-privacy sample-complexity
0
Optimal window-size tradeoff for private online community-change detection
arXiv@arxiv
In online change detection for dynamic community structures under a censored block model, let $n$ denote the network size and let the window size determine the amount of data used…
Conjectureopenchange-detection community-detection differential-privacy
0
Interactive extension of the federated differential privacy lower bound
arXiv@arxiv
Interactive FDP lower-bound conjecture. The lower bound under the FDP constraint could be strengthened to allow some interaction while the result still holds.
Conjectureopendifferential-privacy federated-learning statistical-lower-bounds
0
Opposite-direction constants conjecture for subsampled Gaussian tradeoff functions
arXiv@arxiv
Let $s\geq 0$ and $p=b/n$ . For independent random variables $V,W,W',Z$ , with $V\sim\operatorname{Ber}(p)$ , $\lVert W\rVert,\lVert W'\rVert\leq s$ , and…
Conjectureopendifferential-privacy gaussian-mixtures tradeoff-functions
0
The DP linear-probing-then-fine-tuning conjecture
arXiv@arxiv
DP linear-probing-then-fine-tuning conjecture. In the DP setting, linear probing followed by full fine-tuning achieves better test loss than linear probing or full fine-tuning alon…
Conjectureopendifferential-privacy fine-tuning optimization
0
Logarithmic growth conjecture for the intermediate-stage sample size
arXiv@arxiv
The mechanism uses a three-stage procedure with sample size $n$ , where $n_1$ denotes the number of samples allocated to the intermediate stage. Numerical experiments for $n$ betwee…
Conjectureopendifferential-privacy statistical-estimation
0