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Daniel Hsu

Publications and source records attributed to Daniel Hsu.

At least 37 records · Page 2Linked to original sources
arXiv2025

A Study on the Performance of U-Net Modifications in Retroperitoneal Tumor Segmentation

The retroperitoneum hosts a variety of tumors, including rare benign and malignant types, which pose diagnostic and treatment challenges due to their infrequency and proximity to vital structures. Estimating tumor volume is difficult due to their irregular shapes, and manual segmentation is time-consuming. Automatic segmentation using U-Net and its variants, incorporating Vision Transformer (ViT) elements, has shown promising results but struggles with high computational demands. To address this, architectures like the Mamba State Space Model (SSM) and Extended Long-Short Term Memory (xLSTM) offer efficient solutions by handling long-range dependencies with lower resource consumption. This study evaluates U-Net enhancements, including CNN, ViT, Mamba, and xLSTM, on a new in-house CT dataset and a public organ segmentation dataset. The proposed ViLU-Net model integrates Vi-blocks for improved segmentation. Results highlight xLSTM's efficiency in the U-Net framework. The code is publicly accessible on GitHub.

eess.IV↗
arXiv2024

Efficient Estimation of the Central Mean Subspace via Smoothed Gradient Outer Products

We consider the problem of sufficient dimension reduction (SDR) for multi-index models. The estimators of the central mean subspace in prior works either have slow (non-parametric) convergence rates, or rely on stringent distributional conditions (e.g., the covariate distribution $P_{\mathbf{X}}$ being elliptical symmetric). In this paper, we show that a fast parametric convergence rate of form $C_d \cdot n^{-1/2}$ is achievable via estimating the \emph{expected smoothed gradient outer product}, for a general class of distribution $P_{\mathbf{X}}$ admitting Gaussian or heavier distributions. When the link function is a polynomial with a degree of at most $r$ and $P_{\mathbf{X}}$ is the standard Gaussian, we show that the prefactor depends on the ambient dimension $d$ as $C_d \propto d^r$.

stat.ML↗
arXiv2024

Interactive Machine Teaching by Labeling Rules and Instances

Weakly supervised learning aims to reduce the cost of labeling data by using expert-designed labeling rules. However, existing methods require experts to design effective rules in a single shot, which is difficult in the absence of proper guidance and tooling. Therefore, it is still an open question whether experts should spend their limited time writing rules or instead providing instance labels via active learning. In this paper, we investigate how to exploit an expert's limited time to create effective supervision. First, to develop practical guidelines for rule creation, we conduct an exploratory analysis of diverse collections of existing expert-designed rules and find that rule precision is more important than coverage across datasets. Second, we compare rule creation to individual instance labeling via active learning and demonstrate the importance of both across 6 datasets. Third, we propose an interactive learning framework, INTERVAL, that achieves efficiency by automatically extracting candidate rules based on rich patterns (e.g., by prompting a language model), and effectiveness by soliciting expert feedback on both candidate rules and individual instances. Across 6 datasets, INTERVAL outperforms state-of-the-art weakly supervised approaches by 7% in F1. Furthermore, it requires as few as 10 queries for expert feedback to reach F1 values that existing active learning methods cannot match even with 100 queries.

cs.CL↗
arXiv2024

The piranha problem: Large effects swimming in a small pond

In some scientific fields, it is common to have certain variables of interest that are of particular importance and for which there are many studies indicating a relationship with different explanatory variables. In such cases, particularly those where no relationships are known among the explanatory variables, it is worth asking under what conditions it is possible for all such claimed effects to exist simultaneously. This paper addresses this question by reviewing some theorems from multivariate analysis showing that, unless the explanatory variables also have sizable dependencies with each other, it is impossible to have many such large effects. We discuss implications for the replication crisis in social science.

math.ST↗
arXiv2024

Simple and near-optimal algorithms for hidden stratification and multi-group learning

Multi-group agnostic learning is a formal learning criterion that is concerned with the conditional risks of predictors within subgroups of a population. The criterion addresses recent practical concerns such as subgroup fairness and hidden stratification. This paper studies the structure of solutions to the multi-group learning problem, and provides simple and near-optimal algorithms for the learning problem.

cs.LG↗
arXiv2024

Multi-group Learning for Hierarchical Groups

The multi-group learning model formalizes the learning scenario in which a single predictor must generalize well on multiple, possibly overlapping subgroups of interest. We extend the study of multi-group learning to the natural case where the groups are hierarchically structured. We design an algorithm for this setting that outputs an interpretable and deterministic decision tree predictor with near-optimal sample complexity. We then conduct an empirical evaluation of our algorithm and find that it achieves attractive generalization properties on real datasets with hierarchical group structure.

cs.LG↗
arXiv2024

Transformers Provably Learn Sparse Token Selection While Fully-Connected Nets Cannot

The transformer architecture has prevailed in various deep learning settings due to its exceptional capabilities to select and compose structural information. Motivated by these capabilities, Sanford et al. proposed the sparse token selection task, in which transformers excel while fully-connected networks (FCNs) fail in the worst case. Building upon that, we strengthen the FCN lower bound to an average-case setting and establish an algorithmic separation of transformers over FCNs. Specifically, a one-layer transformer trained with gradient descent provably learns the sparse token selection task and, surprisingly, exhibits strong out-of-distribution length generalization. We provide empirical simulations to justify our theoretical findings.

stat.ML↗
arXiv2024

On the sample complexity of parameter estimation in logistic regression with normal design

The logistic regression model is one of the most popular data generation model in noisy binary classification problems. In this work, we study the sample complexity of estimating the parameters of the logistic regression model up to a given $\ell_2$ error, in terms of the dimension and the inverse temperature, with standard normal covariates. The inverse temperature controls the signal-to-noise ratio of the data generation process. While both generalization bounds and asymptotic performance of the maximum-likelihood estimator for logistic regression are well-studied, the non-asymptotic sample complexity that shows the dependence on error and the inverse temperature for parameter estimation is absent from previous analyses. We show that the sample complexity curve has two change-points in terms of the inverse temperature, clearly separating the low, moderate, and high temperature regimes.

math.ST↗
arXiv2024

Seasonality Patterns in 311-Reported Foodborne Illness Cases and Machine Learning-Identified Indications of Foodborne Illnesses from Yelp Reviews, New York City, 2022-2023

Restaurants are critical venues at which to investigate foodborne illness outbreaks due to shared sourcing, preparation, and distribution of foods. Formal channels to report illness after food consumption, such as 311, New York City's non-emergency municipal service platform, are underutilized. Given this, online social media platforms serve as abundant sources of user-generated content that provide critical insights into the needs of individuals and populations. We extracted restaurant reviews and metadata from Yelp to identify potential outbreaks of foodborne illness in connection with consuming food from restaurants. Because the prevalence of foodborne illnesses may increase in warmer months as higher temperatures breed more favorable conditions for bacterial growth, we aimed to identify seasonal patterns in foodborne illness reports from 311 and identify seasonal patterns of foodborne illness from Yelp reviews for New York City restaurants using a Hierarchical Sigmoid Attention Network (HSAN). We found no evidence of significant bivariate associations between any variables of interest. Given the inherent limitations of relying solely on user-generated data for public health insights, it is imperative to complement these sources with other data streams and insights from subject matter experts. Future investigations should involve conducting these analyses at more granular spatial and temporal scales to explore the presence of such differences or associations.

cs.IR↗
arXiv2024

Distribution-Specific Auditing For Subgroup Fairness

We study the problem of auditing classifiers with the notion of statistical subgroup fairness. Kearns et al. (2018) has shown that the problem of auditing combinatorial subgroups fairness is as hard as agnostic learning. Essentially all work on remedying statistical measures of discrimination against subgroups assumes access to an oracle for this problem, despite the fact that no efficient algorithms are known for it. If we assume the data distribution is Gaussian, or even merely log-concave, then a recent line of work has discovered efficient agnostic learning algorithms for halfspaces. Unfortunately, the reduction of Kearns et al. was formulated in terms of weak, "distribution-free" learning, and thus did not establish a connection for families such as log-concave distributions. In this work, we give positive and negative results on auditing for Gaussian distributions: On the positive side, we present an alternative approach to leverage these advances in agnostic learning and thereby obtain the first polynomial-time approximation scheme (PTAS) for auditing nontrivial combinatorial subgroup fairness: we show how to audit statistical notions of fairness over homogeneous halfspace subgroups when the features are Gaussian. On the negative side, we find that under cryptographic assumptions, no polynomial-time algorithm can guarantee any nontrivial auditing, even under Gaussian feature distributions, for general halfspace subgroups.

cs.LG↗
arXiv2024

Transformers, parallel computation, and logarithmic depth

We show that a constant number of self-attention layers can efficiently simulate, and be simulated by, a constant number of communication rounds of Massively Parallel Computation. As a consequence, we show that logarithmic depth is sufficient for transformers to solve basic computational tasks that cannot be efficiently solved by several other neural sequence models and sub-quadratic transformer approximations. We thus establish parallelism as a key distinguishing property of transformers.

cs.LG↗
arXiv2024

Statistical-Computational Trade-offs in Tensor PCA and Related Problems via Communication Complexity

Tensor PCA is a stylized statistical inference problem introduced by Montanari and Richard to study the computational difficulty of estimating an unknown parameter from higher-order moment tensors. Unlike its matrix counterpart, Tensor PCA exhibits a statistical-computational gap, i.e., a sample size regime where the problem is information-theoretically solvable but conjectured to be computationally hard. This paper derives computational lower bounds on the run-time of memory bounded algorithms for Tensor PCA using communication complexity. These lower bounds specify a trade-off among the number of passes through the data sample, the sample size, and the memory required by any algorithm that successfully solves Tensor PCA. While the lower bounds do not rule out polynomial-time algorithms, they do imply that many commonly-used algorithms, such as gradient descent and power method, must have a higher iteration count when the sample size is not large enough. Similar lower bounds are obtained for Non-Gaussian Component Analysis, a family of statistical estimation problems in which low-order moment tensors carry no information about the unknown parameter. Finally, stronger lower bounds are obtained for an asymmetric variant of Tensor PCA and related statistical estimation problems. These results explain why many estimators for these problems use a memory state that is significantly larger than the effective dimensionality of the parameter of interest.

math.ST↗
arXiv2023

Representational Strengths and Limitations of Transformers

Attention layers, as commonly used in transformers, form the backbone of modern deep learning, yet there is no mathematical description of their benefits and deficiencies as compared with other architectures. In this work we establish both positive and negative results on the representation power of attention layers, with a focus on intrinsic complexity parameters such as width, depth, and embedding dimension. On the positive side, we present a sparse averaging task, where recurrent networks and feedforward networks all have complexity scaling polynomially in the input size, whereas transformers scale merely logarithmically in the input size; furthermore, we use the same construction to show the necessity and role of a large embedding dimension in a transformer. On the negative side, we present a triple detection task, where attention layers in turn have complexity scaling linearly in the input size; as this scenario seems rare in practice, we also present natural variants that can be efficiently solved by attention layers. The proof techniques emphasize the value of communication complexity in the analysis of transformers and related models, and the role of sparse averaging as a prototypical attention task, which even finds use in the analysis of triple detection.

cs.LG↗
arXiv2023

Intrinsic dimensionality and generalization properties of the $\mathcal{R}$-norm inductive bias

We study the structural and statistical properties of $\mathcal{R}$-norm minimizing interpolants of datasets labeled by specific target functions. The $\mathcal{R}$-norm is the basis of an inductive bias for two-layer neural networks, recently introduced to capture the functional effect of controlling the size of network weights, independently of the network width. We find that these interpolants are intrinsically multivariate functions, even when there are ridge functions that fit the data, and also that the $\mathcal{R}$-norm inductive bias is not sufficient for achieving statistically optimal generalization for certain learning problems. Altogether, these results shed new light on an inductive bias that is connected to practical neural network training.

cs.LG↗
arXiv2023

Group conditional validity via multi-group learning

We consider the problem of distribution-free conformal prediction and the criterion of group conditional validity. This criterion is motivated by many practical scenarios including hidden stratification and group fairness. Existing methods achieve such guarantees under either restrictive grouping structure or distributional assumptions, or they are overly-conservative under heteroskedastic noise. We propose a simple reduction to the problem of achieving validity guarantees for individual populations by leveraging algorithms for a problem called multi-group learning. This allows us to port theoretical guarantees from multi-group learning to obtain obtain sample complexity guarantees for conformal prediction. We also provide a new algorithm for multi-group learning for groups with hierarchical structure. Using this algorithm in our reduction leads to improved sample complexity guarantees with a simpler predictor structure.

cs.LG↗
arXiv2022

On the proliferation of support vectors in high dimensions

The support vector machine (SVM) is a well-established classification method whose name refers to the particular training examples, called support vectors, that determine the maximum margin separating hyperplane. The SVM classifier is known to enjoy good generalization properties when the number of support vectors is small compared to the number of training examples. However, recent research has shown that in sufficiently high-dimensional linear classification problems, the SVM can generalize well despite a proliferation of support vectors where all training examples are support vectors. In this paper, we identify new deterministic equivalences for this phenomenon of support vector proliferation, and use them to (1) substantially broaden the conditions under which the phenomenon occurs in high-dimensional settings, and (2) prove a nearly matching converse result.

math.ST↗
arXiv2022

Unbiased estimators for random design regression

In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the sample is drawn i.i.d. from the input distribution, the least squares solution for that sample can be viewed as the natural estimator of the optimum. Unfortunately, this estimator almost always incurs an undesirable bias coming from the randomness of the input points, which is a significant bottleneck in model averaging. In this paper we show that it is possible to draw a non-i.i.d. sample of input points such that, regardless of the response model, the least squares solution is an unbiased estimator of the optimum. Moreover, this sample can be produced efficiently by augmenting a previously drawn i.i.d. sample with an additional set of $d$ points, drawn jointly according to a certain determinantal point process constructed from the input distribution rescaled by the squared volume spanned by the points. Motivated by this, we develop a theoretical framework for studying volume-rescaled sampling, and in the process prove a number of new matrix expectation identities. We use them to show that for any input distribution and $ε>0$ there is a random design consisting of $O(d\log d+ d/ε)$ points from which an unbiased estimator can be constructed whose expected square loss over the entire distribution is bounded by $1+ε$ times the loss of the optimum. We provide efficient algorithms for generating such unbiased estimators in a number of practical settings and support our claims experimentally.

stat.ML↗