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Daniel Li

Daniel Li appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
math.FAInformation RetrievalMachine Learningmath.CAmath.COmath.NTmath.PROther Quantitative Biology

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Published work

18 published item(s)

preprint2026arXiv

Intelligent Elastic Feature Fading: Enabling Model Retrain-Free Feature Efficiency Rollouts at Scale

Large-scale ranking systems depend on thousands of features derived from user behavior across multiple time horizons. Typically requires model retraining -- resulting in long iteration cycles (3--6 months), substantial GPU resource consumption, and limited rollout throughput. We introduce Intelligent Elastic Feature Fading (IEFF), a production infrastructure system that enables retrain-free feature efficiency rollouts by elastically controlling feature coverage and distribution at serving time. IEFF supports incremental feature coverage adjustments while models adapt through recurring training, eliminating dependencies on explicit retraining cycles. The system incorporates strict safety guardrails, reversibility mechanisms, and comprehensive monitoring to ensure stability at scale. Across multiple production use cases, IEFF accelerates efficiency-related rollouts by 5$\times$, eliminates retraining-related GPU overhead, and enables faster capacity recycling. Extensive offline and online experiments demonstrate that gradual feature fading prevents 50--55\% of online performance degradation compared to abrupt feature removal, while maintaining stable model behavior. These results establish elastic, system-level feature fading as a practical and scalable approach for managing feature efficiency in modern industrial ranking systems.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Boundedness of composition operators on general weighted Hardy spaces of analytic functions

We characterize the (essentially) decreasing sequences of positive numbers $β$ = ($β$ n) for which all composition operators on H 2 ($β$) are bounded, where H 2 ($β$) is the space of analytic functions f in the unit disk such that $\infty$ n=0 |c n | 2 $β$ n < $\infty$ if f (z) = $\infty$ n=0 c n z n. We also give conditions for the boundedness when $β$ is not assumed essentially decreasing.

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preprint2020arXiv

Central Limit Theorems for Compound Paths on the 2-Dimensional Lattice

Zeckendorf proved that every integer can be written uniquely as a sum of non-consecutive Fibonacci numbers $\{F_n\}$, and later researchers showed that the distribution of the number of summands needed for such decompositions of integers in $[F_n, F_{n+1})$ converges to a Gaussian as $n\to\infty$. Decomposition problems have been studied extensively for a variety of different sequences and notions of a legal decompositions; for the Fibonacci numbers, a legal decomposition is one for which each summand is used at most once and no two consecutive summands may be chosen. Recently, Chen et al. [CCGJMSY] generalized earlier work to $d$-dimensional lattices of positive integers; there, a legal decomposition is a path such that every point chosen had each component strictly less than the component of the previous chosen point in the path. They were able to prove Gaussianity results despite the lack of uniqueness of the decompositions; however, their results should hold in the more general case where some components are identical. The strictly decreasing assumption was needed in that work to obtain simple, closed form combinatorial expressions, which could then be well approximated and led to the limiting behavior. In this work we remove that assumption through inclusion-exclusion arguments. These lead to more involved combinatorial sums; using generating functions and recurrence relations we obtain tractable forms in $2$ dimensions and prove Gaussianity again; a more involved analysis should work in higher dimensions.

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preprint2020arXiv

Comparison of singular numbers of composition operators on different Hilbert spaces of analytic functions

We compare the rate of decay of singular numbers of a given composition operator acting on various Hilbert spaces of analytic functions on the unit disk $\D$. We show that for the Hardy and Bergman spaces, our results are sharp. We also give lower and upper estimates of the singular numbers of the composition operator with symbol the ``cusp map'' and the lens maps, acting on weighted Dirichlet spaces.

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preprint2020arXiv

Statistical Issues and Recommendations for Clinical Trials Conducted During the COVID-19 Pandemic

The COVID-19 pandemic has had and continues to have major impacts on planned and ongoing clinical trials. Its effects on trial data create multiple potential statistical issues. The scale of impact is unprecedented, but when viewed individually, many of the issues are well defined and feasible to address. A number of strategies and recommendations are put forward to assess and address issues related to estimands, missing data, validity and modifications of statistical analysis methods, need for additional analyses, ability to meet objectives and overall trial interpretability.

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preprint2014arXiv

A spectral radius type formula for approximation numbers of composition operators

For approximation numbers $a_n (C_ϕ)$ of composition operators $C_ϕ$ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol $ϕ$ of uniform norm $< 1$, we prove that $\lim_{n \to \infty} [a_n (C_ϕ)]^{1/n} = \e^{- 1/ \capa [ϕ(\D)]}$, where $\capa [ϕ(\D)]$ is the Green capacity of $ϕ(\D)$ in $\D$. This formula holds also for $H^p$ with $1 \leq p < \infty$.

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preprint2014arXiv

Two remarks on composition operators on the Dirichlet space

We show that the decay of approximation numbers of compact composition operators on the Dirichlet space $\mathcal{D}$ can be as slow as we wish, which was left open in the cited work. We also prove the optimality of a result of O.~El-Fallah, K.~Kellay, M.~Shabankhah and A.~Youssfi on boundedness on $\mathcal{D}$ of self-maps of the disk all of whose powers are norm-bounded in $\mathcal{D}$.

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preprint2012arXiv

Approximation numbers of composition operators on the Dirichlet space

We study the decay of approximation numbers of compact composition operators on the Dirichlet space. We give upper and lower bounds for these numbers. In particular, we improve on a result of O. El-Fallah, K. Kellay, M. Shabankhah and A. Youssfi, on the set of contact points with the unit circle of a compact symbolic composition operator acting on the Dirichlet space D. We extend their results in two directions: first, the contact only takes place at the point 1. Moreover, the approximation numbers of the operator can be arbitrarily sub-exponentially small.

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preprint2012arXiv

Compact composition operators on the Dirichlet space and capacity of sets of contact points

In this paper, we prove that for every compact set of the unit disk of logarithmic capacity 0, there exists a Schur function both in the disk algebra and in the Dirichlet space such that the associated composition operator is in all Schatten classes (of the Dirichlet space), and for which the set of points whose image touches the unit circle is equal to this compact set. We show that for every bounded composition operator on the Dirichlet space and for every point of the unit circle, the logarithmic capacity of the set of point having this point as image is 0. We show that every compact composition operator on the Dirichlet space is compact on the gaussian Hardy-Orlicz space; in particular, it is in every Schatten class on the usual Hilbertian Hardy space. On the other hand, there exists a Schur function such that the associated composition operator is compact on the gaussian Hardy-Orlicz space, but which is not even bounded on the Dirichlet space. We prove that the Schatten classes on the Dirichlet space can be separated by composition operators. Also, there exists a Schur function such that the associated composition operator is compact on the Dirichlet space, but in no Schatten class.

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preprint2012arXiv

Estimates for approximation numbers of some classes of composition operators on the Hardy space

We give estimates for the approximation numbers of composition operators on $H^2$, in terms of some modulus of continuity. For symbols whose image is contained in a polygon, we get that these approximation numbers are dominated by $\e^{- c \sqrt n}$. When the symbol is continuous on the closed unit disk and has a domain touching the boundary non-tangentially at a finite number of points, with a good behavior at the boundary around those points, we can improve this upper estimate. A lower estimate is given when this symbol has a good radial behavior at some point. As an application we get that, for the cusp map, the approximation numbers are equivalent, up to constants, to $\e^{- c \, n / \log n}$, very near to the minimal value $\e^{- c \, n}$. We also see the limitations of our methods. To finish, we improve a result of O. El-Fallah, K. Kellay, M. Shabankhah and H. Youssfi, in showing that for every compact set $K$ of the unit circle $\T$ with Lebesgue measure 0, there exists a compact composition operator $C_ϕ\colon H^2 \to H^2$, which is in all Schatten classes, and such that $ϕ= 1$ on $K$ and $|ϕ| < 1$ outside $K$.

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preprint2012arXiv

Infinitesimal Carleson property for weighted measures induced by analytic self-maps of the unit disk

We prove that, for every $α> -1$, the pull-back measure $ϕ({\cal A}_α)$ of the measure $d{\cal A}_α(z) = (α+ 1) (1 - |z|^2)^α\, d{\cal A} (z)$, where ${\cal A}$ is the normalized area measure on the unit disk $\D$, by every analytic self-map $ϕ\colon \D \to \D$ is not only an $(α+ 2)$-Carleson measure, but that the measure of the Carleson windows of size $\eps h$ is controlled by $\eps^{α+ 2}$ times the measure of the corresponding window of size $h$. This means that the property of being an $(α+ 2)$-Carleson measure is true at all infinitesimal scales. We give an application by characterizing the compactness of composition operators on weighted Bergman-Orlicz spaces.

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preprint2012arXiv

Some new properties of composition operators associated with lens maps

We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space $H^2$. The last ones are connected with Hardy-Orlicz and Bergman-Orlicz spaces $H^ψ$ and $B^ψ$, and provide a negative answer to the question of knowing if all composition operators which are weakly compact on a non-reflexive space are norm-compact.

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preprint2011arXiv

Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces

It is known, from results of B. MacCluer and J. Shapiro (1986), that every composition operator which is compact on the Hardy space $H^p$, $1 \leq p < \infty$, is also compact on the Bergman space ${\mathfrak B}^p = L^p_a (\D)$. In this survey, after having described the above known results, we consider Hardy-Orlicz $H^Ψ$ and Bergman-Orlicz ${\mathfrak B}^Ψ$ spaces, characterize the compactness of their composition operators, and show that there exist Orlicz functions for which there are composition operators which are compact on $H^Ψ$ but not on ${\mathfrak B}^Ψ$.

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preprint2011arXiv

On approximation numbers of composition operators

We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces $\mathfrak{B}_α$ of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they grow at least exponentially, and this speed of convergence is only obtained for symbols which do not approach the unit circle. We also give an upper bounds and explicit an example.

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preprint2010arXiv

Some revisited results about composition operators on Hardy spaces

We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces $H^Ψ$: construction of a "slow" Blaschke product giving a non-compact composition operator on $H^Ψ$; construction of a surjective symbol whose composition operator is compact on $H^Ψ$ and, moreover, is in all the Schatten classes $S_p (H^2)$, $p > 0$. On the other hand, we revisit the classical case of composition operators on $H^2$, giving first a new, and simplier, characterization of closed range composition operators, and then showing directly the equivalence of the two characterizations of membership in the Schatten classes of Luecking and Luecking and Zhu.

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