Prediction of mRNA gene-expression profiles directly from routine whole-slide images (WSIs) using deep learning models could potentially offer cost-effective and widely accessible molecular phenotyping. While such WSI-based gene-expression prediction models have recently emerged within computational pathology, the high-dimensional nature of the corresponding regression problem offers numerous design choices which remain to be analyzed in detail. This study provides recommendations on how deep regression models should be trained for WSI-based gene-expression prediction. For example, we conclude that training a single model to simultaneously regress all 20530 genes is a computationally efficient yet very strong baseline.

The perturbation analysis of linear solvers applied to systems arising broadly in machine learning settings -- for instance, when using linear regression models -- establishes an important perspective when reframing these analyses through the lens of a data poisoning attack. By analyzing solvers' responses to such attacks, this work aims to contribute to the development of more robust linear solvers and provide insights into poisoning attacks on linear solvers. In particular, we investigate how the errors in the input data will affect the fitting error and accuracy of the solution from a linear system-solving algorithm under perturbations common in adversarial attacks. We propose data perturbation through two distinct knowledge levels, developing a poisoning optimization and studying two methods of perturbation: Label-guided Perturbation (LP) and Unconditioning Perturbation (UP). Existing works mainly focus on deriving the worst-case perturbation bound from a theoretical perspective, and the analysis is often limited to specific kinds of linear system solvers. Under the circumstance that the data is intentionally perturbed -- as is the case with data poisoning -- we seek to understand how different kinds of solvers react to these perturbations, identifying those algorithms most impacted by different types of adversarial attacks.

Learning a model of a stochastic setting often involves learning both general structure rules and specific properties of the instance. This paper investigates the interplay between learning the general and the specific in various learning methods, with emphasis on sample efficiency. We design a framework called {\sc LeverWorlds}, which allows the generation of simple physics-inspired worlds that follow a similar generative process with different distributions, and their instances can be expressed in natural language. These worlds allow for controlled experiments to assess the sample complexity of different learning methods. We experiment with classic learning algorithms as well as Transformer language models, both with fine-tuning and In-Context Learning (ICL). Our general finding is that (1) Transformers generally succeed in the task; but (2) they are considerably less sample efficient than classic methods that make stronger assumptions about the structure, such as Maximum Likelihood Estimation and Logistic Regression. This finding is in tension with the recent tendency to use Transformers as general-purpose estimators. We propose an approach that leverages the ICL capabilities of contemporary language models to apply simple algorithms for this type of data. Our experiments show that models currently struggle with the task but show promising potential.

We study high-dimensional, ridge-regularized logistic regression in a setting in which the covariates may be missing or corrupted by additive noise. When both the covariates and the additive corruptions are independent and normally distributed, we provide exact characterizations of both the prediction error as well as the estimation error. Moreover, we show that these characterizations are universal: as long as the entries of the data matrix satisfy a set of independence and moment conditions, our guarantees continue to hold. Universality, in turn, enables the detailed study of several imputation-based strategies when the covariates are missing completely at random. We ground our study by comparing the performance of these strategies with the conjectured performance -- stemming from replica theory in statistical physics -- of the Bayes optimal procedure. Our analysis yields several insights including: (i) a distinction between single imputation and a simple variant of multiple imputation and (ii) that adding a simple ridge regularization term to single-imputed logistic regression can yield an estimator whose prediction error is nearly indistinguishable from the Bayes optimal prediction error. We supplement our findings with extensive numerical experiments.

Large Language Models (LLMs) based on the pre-trained fine-tuning paradigm have become pivotal in solving natural language processing tasks, consistently achieving state-of-the-art performance. Nevertheless, the theoretical understanding of how model complexity influences fine-tuning performance remains challenging and has not been well explored yet. In this paper, we focus on autoregressive LLMs and propose to employ Hidden Markov Models (HMMs) to model them. Based on the HMM modeling, we investigate the relationship between model complexity and the generalization capability in downstream tasks. Specifically, we consider a popular tuning paradigm for downstream tasks, head tuning, where all pre-trained parameters are frozen and only individual heads are trained atop pre-trained LLMs. Our theoretical analysis reveals that the risk initially increases and then decreases with rising model complexity, showcasing a "double descent" phenomenon. In this case, the initial "descent" is degenerate, signifying that the "sweet spot" where bias and variance are balanced occurs when the model size is zero. Obtaining the presented in this study conclusion confronts several challenges, primarily revolving around effectively modeling autoregressive LLMs and downstream tasks, as well as conducting a comprehensive risk analysis for multivariate regression. Our research is substantiated by experiments conducted on data generated from HMMs, which provided empirical support and alignment with our theoretical insights.

Tactile information effectively enables faster training and better task performance for learning-based in-hand manipulation. Existing approaches are validated in simulated environments with a large number of tactile sensors. However, attaching such sensors to a real robot hand is not applicable due to high cost and physical limitations. To enable real-world adoption of tactile sensors, this study investigates the impact of tactile sensors, including their varying quantities and placements on robot hands, on the dexterous manipulation task performance and analyzes the importance of each. Through empirically decreasing the sensor quantities, we successfully find an optimized set of tactile sensors (21 sensors) configuration, which keeps over 93% task performance with only 20% sensor quantities compared to the original set (92 sensors) for the block manipulation task, leading to a potential reduction of over 80% in sensor manufacturing and design costs. To transform the empirical results into a generalizable understanding, we build a task performance prediction model with a weighted linear regression algorithm and use it to forecast the task performance with different sensor configurations. To show its generalizability, we verified this model in egg and pen manipulation tasks and achieved an average prediction error of 3.12%.

Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute Shrinkage and Selection Operator (LASSO) approaches by jointly estimating the permutation, resulting in shuffled LS and shuffled LASSO formulations. Existing methods, constrained by the combinatorial complexity of permutation recovery, often address small-scale cases with limited measurements. In contrast, we focus on large-scale SLR, particularly suited for environments with abundant measurement samples. We propose a spectral matching method that efficiently resolves permutations by aligning spectral components of the measurement and feature covariances. Rigorous theoretical analyses demonstrate that our method achieves accurate estimates in both shuffled LS and shuffled LASSO settings, given a sufficient number of samples. Furthermore, we extend our approach to address simultaneous pose and correspondence estimation in image registration tasks. Experiments on synthetic datasets and real-world image registration scenarios show that our method outperforms existing algorithms in both estimation accuracy and registration performance.

For individuals and families, access to affordable credit is essential as protection against financial volatility, financing and education, pursuing business opportunities, and building equity. From the lender's perspective, there is a delicate balance between improving access to credit and higher costs due to defaults on payments. Creating responsible credit concession models requires maintaining this balance [Kozodoi et al., 2022] while ensuring fair outcomes across different groups of individuals, improving access, and helping applicants understand factors that influence rejection so that they can take action to improve their credit potential. Credit concession models are created using a variety of data, such as employment history (for example, occupation and income), demographic data (such as age, marital status, and education), and financial data (for example, checking account balance, credit card usage, and bill payment history). Given these features, models such as logistic regression, gradient boosting, and decision trees can be trained to predict whether a new customer will default on a loan over a period of time [Louzada et al., 2016].

The human visual system is capable of processing continuous streams of visual information, but how the brain encodes and retrieves recent visual memories during continuous visual processing remains unexplored. This study investigates the capacity of working memory to retain past information under continuous visual stimuli. And then we propose a new task Memory Disentangling, which aims to extract and decode past information from fMRI signals. To address the issue of interference from past memory information, we design a disentangled contrastive learning method inspired by the phenomenon of proactive interference. This method separates the information between adjacent fMRI signals into current and past components and decodes them into image descriptions. Experimental results demonstrate that this method effectively disentangles the information within fMRI signals. This research could advance brain-computer interfaces and mitigate the problem of low temporal resolution in fMRI.

Random forests have become popular for clinical risk prediction modelling. In a case study on predicting ovarian malignancy, we observed training c-statistics close to 1. Although this suggests overfitting, performance was competitive on test data. We aimed to understand the behaviour of random forests by (1) visualizing data space in three real world case studies and (2) a simulation study. For the case studies, risk estimates were visualised using heatmaps in a 2-dimensional subspace. The simulation study included 48 logistic data generating mechanisms (DGM), varying the predictor distribution, the number of predictors, the correlation between predictors, the true c-statistic and the strength of true predictors. For each DGM, 1000 training datasets of size 200 or 4000 were simulated and RF models trained with minimum node size 2 or 20 using ranger package, resulting in 192 scenarios in total. The visualizations suggested that the model learned spikes of probability around events in the training set. A cluster of events created a bigger peak, isolated events local peaks. In the simulation study, median training c-statistics were between 0.97 and 1 unless there were 4 or 16 binary predictors with minimum node size 20. Median test c-statistics were higher with higher events per variable, higher minimum node size, and binary predictors. Median training slopes were always above 1, and were not correlated with median test slopes across scenarios (correlation -0.11). Median test slopes were higher with higher true c-statistic, higher minimum node size, and higher sample size. Random forests learn local probability peaks that often yield near perfect training c-statistics without strongly affecting c-statistics on test data. When the aim is probability estimation, the simulation results go against the common recommendation to use fully grown trees in random forest models.