arXiv subjects

Jane H. Lee

Publications and source records attributed to Jane H. Lee.

6 recordsLinked to original sources

arXiv2026

Smoothed Analysis of Learning from Positive Samples

Binary classification from positive-only samples is a variant of PAC learning where the learner receives i.i.d. positive samples and aims to learn a classifier with low error. Previous work by Natarajan, Gereb-Graus, and Shvaytser characterized learnability and revealed a largely negative picture: almost no interesting classes, including two-dimensional halfspaces, are learnable. This poses a challenge for applications from bioinformatics to ecology, where practitioners rely on heuristics. In this work, we initiate a smoothed analysis of positive-only learning. We assume samples from a reference distribution $D$ such that the true distribution $D^*$ is smooth with respect to it. In stark contrast to the worst-case setting, we show that all VC classes become learnable in the smoothed model, requiring $O(VC/ε^2)$ positive samples for $ε$ classification error. We also give an efficient algorithm for any class admitting $\mathrm{poly}(ε)$-approximation by degree-$k$ polynomials whose range is lower-bounded by a constant with respect to $D$ in L1-norm. It runs in time $\mathrm{poly}(d^k/ε)$, qualitatively matching L1-regression. Our results also imply faster or more general algorithms for: (1) estimation with unknown-truncation, giving the first polynomial-time algorithm for estimating exponential-family parameters from samples truncated to an unknown set approximable by non-negative polynomials in L1 norm, improving on [KTZ FOCS19; LMZ FOCS24], who required strong L2-approximation; (2) truncation detection for broad classes, including non-product distributions, improving on [DLNS STOC24]'s who required product distributions; and (3) learning from a list of reference distributions, where samples come from $O(1)$ distributions, one of which witnesses smoothness of $D^*$, as arises when list-decoding algorithms learn samplers for $D^*$ from corrupted data.

stat.ML↗

arXiv2026

Efficient Statistics With Unknown Truncation, Polynomial Time Algorithms, Beyond Gaussians

We study the estimation of distributional parameters when samples are shown only if they fall in some unknown set $S \subseteq \mathbb{R}^d$. Kontonis, Tzamos, and Zampetakis (FOCS'19) gave a $d^{\mathrm{poly}(1/\varepsilon)}$ time algorithm for finding $\varepsilon$-accurate parameters for the special case of Gaussian distributions with diagonal covariance matrix. Recently, Diakonikolas, Kane, Pittas, and Zarifis (COLT'24) showed that this exponential dependence on $1/\varepsilon$ is necessary even when $S$ belongs to some well-behaved classes. These works leave the following open problems which we address in this work: Can we estimate the parameters of any Gaussian or even extend beyond Gaussians? Can we design $\mathrm{poly}(d/\varepsilon)$ time algorithms when $S$ is a simple set such as a halfspace? We make progress on both of these questions by providing the following results: 1. Toward the first question, we give a $d^{\mathrm{poly}(\ell/\varepsilon)}$ time algorithm for any exponential family that satisfies some structural assumptions and any unknown set $S$ that is $\varepsilon$-approximable by degree-$\ell$ polynomials. This result has two important applications: 1a) The first algorithm for estimating arbitrary Gaussian distributions from samples truncated to an unknown $S$; and 1b) The first algorithm for linear regression with unknown truncation and Gaussian features. 2. To address the second question, we provide an algorithm with runtime $\mathrm{poly}(d/\varepsilon)$ that works for a set of exponential families (containing all Gaussians) when $S$ is a halfspace or an axis-aligned rectangle. Along the way, we develop tools that may be of independent interest, including, a reduction from PAC learning with positive and unlabeled samples to PAC learning with positive and negative samples that is robust to certain covariate shifts.

math.ST↗

arXiv2026

A Note on Non-Negative $L_1$-Approximating Polynomials

$L_1$-Approximating polynomials, i.e., polynomials that approximate indicator functions in $L_1$-norm under certain distributions, are widely used in computational learning theory. We study the existence of \textit{non-negative} $L_1$-approximating polynomials with respect to Gaussian distributions. This is a stronger requirement than $L_1$-approximation but weaker than sandwiching polynomials (which themselves have many applications). These non-negative approximating polynomials have recently found uses in smoothed learning from positive-only examples. In this short note, we prove that every class of sets with Gaussian surface area (GSA) at most $Γ$ under the standard Gaussian admits degree-$k$ non-negative polynomials that $\eps$-approximate its indicator functions in $L_1$-norm, for $k=\tilde{O}(Γ^2/\varepsilon^2)$. Equivalently, finite GSA implies $L_1$-approximation with the stronger pointwise guarantee that the approximating polynomial has range contained in $[0,\infty)$. Up to a constant-factor, this matches the degree of the best currently known Gaussian $L_1$-approximation degree bound without the non-negativity constraint.

stat.ML↗

arXiv2026

Massive Memorization with Hundreds of Trillions of Parameters for Sequential Transducer Generative Recommenders

Modern large-scale recommendation systems rely heavily on user interaction history sequences to enhance the model performance. The advent of large language models and sequential modeling techniques, particularly transformer-like architectures, has led to significant advancements recently (e.g., HSTU, SIM, and TWIN models). While scaling to ultra-long user histories (10k to 100k items) generally improves model performance, it also creates significant challenges on latency, queries per second (QPS) and GPU cost in industry-scale recommendation systems. Existing models do not adequately address these industrial scalability issues. In this paper, we propose a novel two-stage modeling framework, namely VIrtual Sequential Target Attention (VISTA), which decomposes traditional target attention from a candidate item to user history items into two distinct stages: (1) user history summarization into a few hundred tokens; followed by (2) candidate item attention to those tokens. These summarization token embeddings are then cached in storage system and then utilized as sequence features for downstream model training and inference. This novel design for scalability enables VISTA to scale to lifelong user histories (up to one million items) while keeping downstream training and inference costs fixed, which is essential in industry. Our approach achieves significant improvements in offline and online metrics and has been successfully deployed on an industry leading recommendation platform serving billions of users.

cs.IR↗

arXiv2025

Risk-Averse Constrained Reinforcement Learning with Optimized Certainty Equivalents

Constrained optimization provides a common framework for dealing with conflicting objectives in reinforcement learning (RL). In most of these settings, the objectives (and constraints) are expressed though the expected accumulated reward. However, this formulation neglects risky or even possibly catastrophic events at the tails of the reward distribution, and is often insufficient for high-stakes applications in which the risk involved in outliers is critical. In this work, we propose a framework for risk-aware constrained RL, which exhibits per-stage robustness properties jointly in reward values and time using optimized certainty equivalents (OCEs). Our framework ensures an exact equivalent to the original constrained problem within a parameterized strong Lagrangian duality framework under appropriate constraint qualifications, and yields a simple algorithmic recipe which can be wrapped around standard RL solvers, such as PPO. Lastly, we establish the convergence of the proposed algorithm under common assumptions, and verify the risk-aware properties of our approach through several numerical experiments.

cs.LG↗

arXiv2023

Exact Gradient Computation for Spiking Neural Networks Through Forward Propagation

Spiking neural networks (SNN) have recently emerged as alternatives to traditional neural networks, owing to energy efficiency benefits and capacity to better capture biological neuronal mechanisms. However, the classic backpropagation algorithm for training traditional networks has been notoriously difficult to apply to SNN due to the hard-thresholding and discontinuities at spike times. Therefore, a large majority of prior work believes exact gradients for SNN w.r.t. their weights do not exist and has focused on approximation methods to produce surrogate gradients. In this paper, (1) by applying the implicit function theorem to SNN at the discrete spike times, we prove that, albeit being non-differentiable in time, SNNs have well-defined gradients w.r.t. their weights, and (2) we propose a novel training algorithm, called \emph{forward propagation} (FP), that computes exact gradients for SNN. FP exploits the causality structure between the spikes and allows us to parallelize computation forward in time. It can be used with other algorithms that simulate the forward pass, and it also provides insights on why other related algorithms such as Hebbian learning and also recently-proposed surrogate gradient methods may perform well.

cs.NE↗