NeurIPS 2024 论文列表

We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a "query" distribution $q$ over $[n]$, output $p_i$ that is "close" to $q$. Recently Aamand et al. gave the first and only known result that achieves sublinear bounds in both the sampling complexity and the query time while preserving polynomial data structure space. However, their improvement over linear samples and time is only by subpolynomial factors. Our main result is a lower bound showing that, for a broad class of data structures, their bounds cannot be significantly improved. In particular, if an algorithm uses $O(n/\log^c k)$ samples for some constant $c>0$ and polynomial space, then the query time of the data structure must be at least $k^{1-O(1)/\log \log k}$, i.e., close to linear in the number of distributions $k$. This is a novel statistical-computational trade-off for density estimation, demonstrating that any data structure must use close to a linear number of samples or take close to linear query time. The lower bound holds even in the realizable case where $q=p_i$ for some $i$, and when the distributions are flat (specifically, all distributions are uniform over half of the domain $[n]$). We also give a simple data structure for our lower bound instance with asymptotically matching upper bounds. Experiments show that the data structure is quite efficient in practice.

In recent years, transformer-based models have revolutionized deep learning, particularly in sequence modeling. To better understand this phenomenon, there is a growing interest in using Markov input processes to study transformers. However, our current understanding in this regard remains limited with many fundamental questions about how transformers learn Markov chains still unanswered. In this paper, we address this by focusing on first-order Markov chains and single-layer transformers, providing a comprehensive characterization of the learning dynamics in this context. Specifically, we prove that transformer parameters trained on next-token prediction loss can either converge to global or local minima, contingent on the initialization and the Markovian data properties, and we characterize the precise conditions under which this occurs. To the best of our knowledge, this is the first result of its kind highlighting the role of initialization. We further demonstrate that our theoretical findings are corroborated by empirical evidence. Based on these insights, we provide guidelines for the initialization of single-layer transformers and demonstrate their effectiveness. Finally, we outline several open problems in this arena. Code is available at: \url{https://github.com/Bond1995/Markov}.

Amino acid substitution rate matrices are fundamental to statistical phylogenetics and evolutionary biology. Estimating them typically requires reconstructed trees for massive amounts of aligned proteins, which poses a major computational bottleneck. In this paper, we develop a near-linear time method to estimate these rate matrices from multiple sequence alignments (MSAs) alone, thereby speeding up computation by orders of magnitude. Our method relies on a near-linear time cherry reconstruction algorithm which we call FastCherries and it can be easily applied to MSAs with millions of sequences. On both simulated and real data, we demonstrate the speed and accuracy of our method as applied to the classical model of protein evolution. By leveraging the unprecedented scalability of our method, we develop a new, rich phylogenetic model called SiteRM, which can estimate a general site-specific rate matrix for each column of an MSA. Remarkably, in variant effect prediction for both clinical and deep mutational scanning data in ProteinGym, we show that despite being an independent-sites model, our SiteRM model outperforms large protein language models that learn complex residue-residue interactions between different sites. We attribute our increased performance to conceptual advances in our probabilistic treatment of evolutionary data and our ability to handle extremely large MSAs. We anticipate that our work will have a lasting impact across both statistical phylogenetics and computational variant effect prediction. FastCherries and SiteRM are implemented in the CherryML package https://github.com/songlab-cal/CherryML.

Estimating individualized treatment rules (ITRs) is fundamental in causal inference, particularly for precision medicine applications. Traditional ITR estimation methods rely on inverse probability weighting (IPW) to address confounding factors and $L_{1}$-penalization for simplicity and interpretability. However, IPW can introduce statistical bias without precise propensity score modeling, while $L_1$-penalization makes the objective non-smooth, leading to computational bias and requiring subgradient methods. In this paper, we propose a unified ITR estimation framework formulated as a constrained, weighted, and smooth convex optimization problem. The optimal ITR can be robustly and effectively computed by projected gradient descent. Our comprehensive theoretical analysis reveals that weights that balance the spectrum of a `weighted design matrix' improve both the optimization and likelihood landscapes, yielding improved computational and statistical estimation guarantees. In particular, this is achieved by distributional covariate balancing weights, which are model-free alternatives to IPW. Extensive simulations and applications demonstrate that our framework achieves significant gains in both robustness and effectiveness for ITR learning against existing methods.

We consider sequential treatment regimes where each unit is exposed to combinations of interventions over time. When interventions are described by qualitative labels, such as "close schools for a month due to a pandemic" or "promote this podcast to this user during this week", it is unclear which appropriate structural assumptions allow us to generalize behavioral predictions to previously unseen combinations of interventions. Standard black-box approaches mapping sequences of categorical variables to outputs are applicable, but they rely on poorly understood assumptions on how reliable generalization can be obtained, and may underperform under sparse sequences, temporal variability, and large action spaces. To approach that, we pose an explicit model for composition, that is, how the effect of sequential interventions can be isolated into modules, clarifying which data conditions allow for the identification of their combined effect at different units and time steps. We show the identification properties of our compositional model, inspired by advances in causal matrix factorization methods. Our focus is on predictive models for novel compositions of interventions instead of matrix completion tasks and causal effect estimation. We compare our approach to flexible but generic black-box models to illustrate how structure aids prediction in sparse data conditions.

Optogenetics is widely used to study the effects of neural circuit manipulation on behavior. However, the paucity of causal inference methodological work on this topic has resulted in analysis conventions that discard information, and constrain the scientific questions that can be posed. To fill this gap, we introduce a nonparametric causal inference framework for analyzing "closed-loop" designs, which use dynamic policies that assign treatment based on covariates. In this setting, standard methods can introduce bias and occlude causal effects. Building on the sequentially randomized experiments literature in causal inference, our approach extends history-restricted marginal structural models for dynamic regimes. In practice, our framework can identify a wide range of causal effects of optogenetics on trial-by-trial behavior, such as, fast/slow-acting, dose-response, additive/antagonistic, and floor/ceiling. Importantly, it does so without requiring negative controls, and can estimate how causal effect magnitudes evolve across time points. From another view, our work extends "excursion effect" methods---popular in the mobile health literature---to enable estimation of causal contrasts for treatment sequences greater than length one, in the presence of positivity violations. We derive rigorous statistical guarantees, enabling hypothesis testing of these causal effects. We demonstrate our approach on data from a recent study of dopaminergic activity on learning, and show how our method reveals relevant effects obscured in standard analyses.

Conditional density estimation (CDE) goes beyond regression by modeling the full conditional distribution, providing a richer understanding of the data than just the conditional mean in regression. This makes CDE particularly useful in critical application domains. However, interpretable CDE methods are understudied. Current methods typically employ kernel-based approaches, using kernel functions directly for kernel density estimation or as basis functions in linear models. In contrast, despite their conceptual simplicity and visualization suitability, tree-based methods---which are arguably more comprehensible---have been largely overlooked for CDE tasks. Thus, we propose the Conditional Density Tree (CDTree), a fully non-parametric model consisting of a decision tree in which each leaf is formed by a histogram model. Specifically, we formalize the problem of learning a CDTree using the minimum description length (MDL) principle, which eliminates the need for tuning the hyperparameter for regularization. Next, we propose an iterative algorithm that, although greedily, searches the optimal histogram for every possible node split. Our experiments demonstrate that, in comparison to existing interpretable CDE methods, CDTrees are both more accurate (as measured by the log-loss) and more robust against irrelevant features. Further, our approach leads to smaller tree sizes than existing tree-based models, which benefits interpretability.

Understanding treatment effect heterogeneity is vital for scientific and policy research. However, identifying and evaluating heterogeneous treatment effects pose significant challenges due to the typically unknown subgroup structure. Recently, a novel approach, causal k-means clustering, has emerged to assess heterogeneity of treatment effect by applying the k-means algorithm to unknown counterfactual regression functions. In this paper, we expand upon this framework by integrating hierarchical and density-based clustering algorithms. We propose plug-in estimators which are simple and readily implementable using off-the-shelf algorithms. Unlike k-means clustering, which requires the margin condition, our proposed estimators do not rely on strong structural assumptions on the outcome process. We go on to study their rate of convergence, and show that under the minimal regularity conditions, the additional cost of causal clustering is essentially the estimation error of the outcome regression functions. Our findings significantly extend the capabilities of the causal clustering framework, thereby contributing to the progression of methodologies for identifying homogeneous subgroups in treatment response, consequently facilitating more nuanced and targeted interventions. The proposed methods also open up new avenues for clustering with generic pseudo-outcomes. We explore finite sample properties via simulation, and illustrate the proposed methods in voting and employment projection datasets.

Identifying subgroups with differential responses to treatment is pivotal in randomized clinical trials, as tailoring treatments to specific subgroups can advance personalized medicine. Upon trial completion, identifying best-performing subgroups–those with the most beneficial treatment effects–is crucial for optimizing resource allocation or mitigating adverse treatment effects. However, traditional clinical trials are not customized for the goal of identifying best-performing subgroups because they typically pre-define subgroups at the beginning of the trial and adhere to a fixed subgroup treatment allocation rule, leading to inefficient use of experimental efforts. While some adaptive experimental strategies exist for the identification of the single best subgroup, they commonly do not enable the identification of the best set of subgroups. To address these challenges, we propose a dynamic subgroup identification covariate-adjusted response-adaptive randomization (CARA) design strategy with the following key features: (i) Our approach is an adaptive experimental strategy that allows the dynamic identification of the best subgroups and the revision of treatment allocation towards the goal of correctly identifying the best subgroups based on collected experimental data. (ii) Our design handles ties between subgroups effectively, merging those with similar treatment effects to maximize experimental efficiency. In the theoretical investigations, we demonstrate that our design has a higher probability of correctly identifying the best set of subgroups compared to conventional designs. Additionally, we prove the statistical validity of our estimator for the best subgroup treatment effect, demonstrating its asymptotic normality and semiparametric efficiency. Finally, we validate our design using synthetic data from a clinical trial on cirrhosis.

Accurate estimation of treatment effects is essential for decision-making across various scientific fields. This task, however, becomes challenging in areas like social sciences and online marketplaces, where treating one experimental unit can influence outcomes for others through direct or indirect interactions. Such interference can lead to biased treatment effect estimates, particularly when the structure of these interactions is unknown. We address this challenge by introducing a new class of estimators based on causal message-passing, specifically designed for settings with pervasive, unknown interference. Our estimator draws on information from the sample mean and variance of unit outcomes and treatments over time, enabling efficient use of observed data to estimate the evolution of the system state. Concretely, we construct non-linear features from the moments of unit outcomes and treatments and then learn a function that maps these features to future mean and variance of unit outcomes. This allows for the estimation of the treatment effect over time. Extensive simulations across multiple domains, using synthetic and real network data, demonstrate the efficacy of our approach in estimating total treatment effect dynamics, even in cases where interference exhibits non-monotonic behavior in the probability of treatment.

Estimating the effect of treatments from natural experiments, where treatments are pre-assigned, is an important and well-studied problem. We introduce a novel natural experiment dataset obtained from an early childhood literacy nonprofit. Surprisingly, applying over 20 established estimators to the dataset produces inconsistent results in evaluating the nonprofits efficacy. To address this, we create a benchmark to evaluate estimator accuracy using synthetic outcomes, whose design was guided by domain experts. The benchmark extensively explores performance as real world conditions like sample size, treatment correlation, and propensity score accuracy vary. Based on our benchmark, we observe that the class of doubly robust treatment effect estimators, which are based on simple and intuitive regression adjustment, generally outperform other more complicated estimators by orders of magnitude. To better support our theoretical understanding of doubly robust estimators, we derive a closed form expression for the variance of any such estimator that uses dataset splitting to obtain an unbiased estimate. This expression motivates the design of a new doubly robust estimator that uses a novel loss function when fitting functions for regression adjustment. We release the dataset and benchmark in a Python package; the package is built in a modular way to facilitate new datasets and estimators. https://github.com/rtealwitter/naturalexperiments