24 problems

The low-entropy conjecture for classifiers generated by boosting
arXiv@arxiv
Let ${\cal H}$ be a class of base classifiers and let ${\rm conv}({\cal H})$ denote its convex hull. Consider classifiers obtained in consecutive rounds of boosting, and let…
Conjectureopenboosting empirical-processes statistical-learning-theory
0
Conjecture on improving the partitioning classification excess-risk bound
arXiv@arxiv
Let $H_x$ be the distribution function associated with the predictor value $x\in\mathcal{X}$ , and suppose that $H_x$ is continuous for every $x$ . Let $m$ satisfy the generalized Li…
Conjectureopenbinary-classification convergence-rates statistical-learning-theory
0
Rudelson–Vershynin logarithmic metric-entropy conjecture
arXiv@arxiv
Let a bounded real-valued function class have finite $gamma$ -fat-shattering dimension, and consider the covering-number or metric-entropy bound obtained at the relevant scale. **R…
Conjectureopenfat-shattering metric-entropy statistical-learning-theory
0
Alon et al.'s metric-entropy logarithm conjecture
arXiv@arxiv
Let $gamma0$ and let $the gamma$ -fat-shattering dimension of a bounded real-valued function class be finite. Consider the metric entropy of the class at the relevant scale, measu…
Conjectureopenfat-shattering metric-entropy statistical-learning-theory
0
Phil Long's conjecture that the factor-of-two gap is unavoidable
arXiv@arxiv
In real-valued statistical learning, the $gamma$ -fat-shattering dimension controls learnability and uniform convergence only up to a possible factor of $2$ in the scale. Phil Long'…
Conjectureopenfat-shattering statistical-learning-theory uniform-convergence
0
The interpolation-objective conjecture for flow matching on manifolds
arXiv@arxiv
Flow matching with linear interpolation is trained using an interpolation-based objective, and its convergence rate has a support-estimation component that is slower than the optim…
Conjectureopenflow-matching manifold-learning statistical-learning-theory
0
The uncomputable-hypothesis conjecture for CPAC learning
arXiv@arxiv
Let $\mathcal{H}$ be a hypothesis class, and let $\operatorname{eVCdim}(\mathcal{H})$ denote its effective VC-dimension. A hypothesis in $\mathcal{H}$ is uncomputable if it is not…
Conjectureopencomputable-learning-theory effective-vc-dimension statistical-learning-theory
0
Maximal-power conjecture for the transition in multi-class stochastic gradient descent
arXiv@arxiv
The setting is the two-class stochastic-gradient-descent model discussed above, with power-law covariance and mean parameters whose exponents include $\alpha$ ; the relevant transit…
Conjectureopenpower-law-models statistical-learning-theory stochastic-gradient-descent
1
Gaussian fixed-point conjecture for optimal tradeoff and sample complexity
arXiv@arxiv
Let $F$ be a class of functions, let $D$ denote the unit ball of $L_2(\mu)$ , and let $r_{\mathbb{Q}}(\kappa)$ and $r_{\mathbb{M}}(\kappa)$ be the Gaussian fixed points defined by ……
Conjectureopenempirical-processes sample-complexity statistical-learning-theory
0
Multiclass logistic-regression logit truncation conjecture
arXiv@arxiv
Let $K\geq 3$ . In the $K$ -class setting, let $\widehat{\boldsymbol{f}}(\text{\boldmath$ x $}_i)\in\mathbb{R}^K$ denote the multinomial logistic-regression logits for the observed fe…
Conjectureopenlogistic-regression multiclass-classification statistical-learning-theory
1
Existence and uniqueness of the fixed-point solution for regularized M-estimators
arXiv@arxiv
Existence and uniqueness conjecture. These assumptions are sufficient to guarantee existence and uniqueness of a solution to the system, without requiring the loss and penalty to b…
Conjectureopenfixed-point-equations m-estimators statistical-learning-theory
0
Replica-method validity for the paper's asymptotic feature-learning results
arXiv@arxiv
The paper considers the asymptotic limit $N\to\infty$ for feature learning in imbalanced classification, using the mathematically non-rigorous replica method to derive results abou…
Conjectureopenimbalanced-classification replica-method statistical-learning-theory
0
The min-norm regularization conjecture for overparameterized estimators
arXiv@arxiv
Min-norm interpolators and estimators are considered in an overparameterized regime, where the number of parameters may exceed the number of observations and interpolation is possi…
Conjectureopenoverparameterization regularization statistical-learning-theory
0
Improved expected coverage bound for QQM
arXiv@arxiv
Let $m$ and $n$ denote the parameters governing the federated conformal prediction setting, let $\beta$ be the target miscoverage level, and let $\text{QQM}$ denote the QQM algorit…
Conjectureopenconformal-prediction federated-learning statistical-learning-theory
0
Bruckstein–Cover lower-bound conjecture for linear separability
arXiv@arxiv
Let $S(n,p)$ denote the probability that $n$ labeled observations in $\boldsymbol{R}^p$ are linearly separable, and let … be the value in Cover's identity for the corresponding sym…
Conjectureopenlinear-separability probability statistical-learning-theory
0
Daniely–Shalev-Shwartz conjecture on DS dimension and risk complexity
arXiv@arxiv
Let $\mathcal{H} \subseteq \mathcal{Y}^{\mathcal{X}}$ be a hypothesis class with Daniely–Shalev-Shwartz dimension $d_{\operatorname{DS}}$ , and let $(d_n)_{n \in \mathbb{N}}$ be the…
Conjecturerefutedcomplexity-dimensions pac-learning statistical-learning-theory
1
Information-theoretic conjecture for tight excess-risk bounds in VC classes
arXiv@arxiv
Let $\mathcal{H}$ be a class of functions with finite VC-dimension $D$ , and let $W$ , $X^n$ , and $Y^n$ denote the random variables in the Bayesian realizable classification setting…
Conjectureopeninformation-theory statistical-learning-theory vc-dimension
1
Exponential convergence conjecture for VC-dimension model selection
arXiv@arxiv
The model-selection setting involves an estimator $\hat{d}_{VC}$ of the VC dimension $d_{VC}$ , with convergence measured in probability. The existing result gives only a rate of or…
Conjectureopenmodel-selection statistical-learning-theory vc-dimension
0
The conjecture that no universally consistent rule is smart
arXiv@arxiv
Let $(g_n)$ be a learning rule for binary classification. It is universally consistent if it is weakly consistent and strongly consistent for every probability measure $\mu$ on…
Conjectureopenconsistency statistical-learning-theory
0
Conjecture on counterexamples to fast rates for maximum regularized likelihood estimators
arXiv@arxiv
Maximum regularized likelihood estimators are considered in the general prediction setting, including regression, where assumptionless oracle inequalities have been established and…
Conjectureopenmaximum-likelihood-estimation oracle-inequalities statistical-learning-theory
0
Bayes-consistency conjecture for GKN
arXiv@arxiv
Let textup{{textsf{GKN}}} be the earlier gamma-net-based classification algorithm described in the paper, which removes a minimum vertex cover so that the remaining sample is gamma…
Conjectureopennearest-neighbor-methods sample-compression statistical-learning-theory
0
Refined label-complexity upper bound for Bernstein classes
arXiv@arxiv
Let $cmathbb{C}$ be a binary hypothesis class with VC dimension $d$ and star number $\mathfrak{s}$ . For $a dots$ and $mathcal{P}$ satisfying the Bernstein condition with parameters…
Conjectureopenactive-learning label-complexity statistical-learning-theory
0
Extension of the minimax lower bound to all margin exponents
arXiv@arxiv
The paper considers classification with errors in variables, under a noise assumption, and studies estimators of the optimal discriminant set $G_K^{\star}$ over the class…
Conjectureopenclassification errors-in-variables statistical-learning-theory
1
Conjecture on the optimal active-learning excess-risk rate
arXiv@arxiv
Rate conjecture. The correct rate of convergence for the excess risk is
Conjectureopenactive-learning nonparametric-statistics statistical-learning-theory
0