In this note, we consider the problem of robust learning mixtures of linear regressions. We connect mixtures of linear regressions and mixtures of Gaussians with a simple thresholding, so that a quasi-polynomial time algorithm can be obtained under some mild separation condition. This algorithm has significantly better robustness than the previous result.

Post-selection inference (PoSI) is a statistical technique for obtaining valid confidence intervals and p-values when hypothesis generation and testing use the same source of data. PoSI can be used on a range of popular algorithms including the Lasso. Data carving is a variant of PoSI in which a portion of held out data is combined with the hypothesis generating data at inference time. While data carving has attractive theoretical and empirical properties, existing approaches rely on computationally expensive MCMC methods to carry out inference. This paper's key contribution is to show that pivotal quantities can be constructed for the data carving procedure based on a known parametric distribution. Specifically, when the selection event is characterized by a set of polyhedral constraints on a Gaussian response, data carving will follow the sum of a normal and a truncated normal (SNTN), which is a variant of the truncated bivariate normal distribution. The main impact of this insight is that obtaining exact inference for data carving can be made computationally trivial, since the CDF of the SNTN distribution can be found using the CDF of a standard bivariate normal. A python package sntn has been released to further facilitate the adoption of data carving with PoSI.

Supervised dimension reduction (SDR) has been a topic of growing interest in data science, as it enables the reduction of high-dimensional covariates while preserving the functional relation with certain response variables of interest. However, existing SDR methods are not suitable for analyzing datasets collected from case-control studies. In this setting, the goal is to learn and exploit the low-dimensional structure unique to or enriched by the case group, also known as the foreground group. While some unsupervised techniques such as the contrastive latent variable model and its variants have been developed for this purpose, they fail to preserve the functional relationship between the dimension-reduced covariates and the response variable. In this paper, we propose a supervised dimension reduction method called contrastive inverse regression (CIR) specifically designed for the contrastive setting. CIR introduces an optimization problem defined on the Stiefel manifold with a non-standard loss function. We prove the convergence of CIR to a local optimum using a gradient descent-based algorithm, and our numerical study empirically demonstrates the improved performance over competing methods for high-dimensional data.

We present an effective framework for improving the breakdown point of robust regression algorithms. Robust regression has attracted widespread attention due to the ubiquity of outliers, which significantly affect the estimation results. However, many existing robust least-squares regression algorithms suffer from a low breakdown point, as they become stuck around local optima when facing severe attacks. By expanding on the previous work, we propose a novel framework that enhances the breakdown point of these algorithms by inserting a prior distribution in each iteration step, and adjusting the prior distribution according to historical information. We apply this framework to a specific algorithm and derive the consistent robust regression algorithm with iterative local search (CORALS). The relationship between CORALS and momentum gradient descent is described, and a detailed proof of the theoretical convergence of CORALS is presented. Finally, we demonstrate that the breakdown point of CORALS is indeed higher than that of the algorithm from which it is derived. We apply the proposed framework to other robust algorithms, and show that the improved algorithms achieve better results than the original algorithms, indicating the effectiveness of the proposed framework.

Objective: Evictions are important social and behavioral determinants of health. Evictions are associated with a cascade of negative events that can lead to unemployment, housing insecurity/homelessness, long-term poverty, and mental health problems. In this study, we developed a natural language processing system to automatically detect eviction status from electronic health record (EHR) notes. Materials and Methods: We first defined eviction status (eviction presence and eviction period) and then annotated eviction status in 5000 EHR notes from the Veterans Health Administration (VHA). We developed a novel model, KIRESH, that has shown to substantially outperform other state-of-the-art models such as fine-tuning pre-trained language models like BioBERT and BioClinicalBERT. Moreover, we designed a novel prompt to further improve the model performance by using the intrinsic connection between the two sub-tasks of eviction presence and period prediction. Finally, we used the Temperature Scaling-based Calibration on our KIRESH-Prompt method to avoid over-confidence issues arising from the imbalance dataset. Results: KIRESH-Prompt substantially outperformed strong baseline models including fine-tuning the BioClinicalBERT model to achieve 0.74672 MCC, 0.71153 Macro-F1, and 0.83396 Micro-F1 in predicting eviction period and 0.66827 MCC, 0.62734 Macro-F1, and 0.7863 Micro-F1 in predicting eviction presence. We also conducted additional experiments on a benchmark social determinants of health (SBDH) dataset to demonstrate the generalizability of our methods. Conclusion and Future Work: KIRESH-Prompt has substantially improved eviction status classification. We plan to deploy KIRESH-Prompt to the VHA EHRs as an eviction surveillance system to help address the US Veterans' housing insecurity.

We revisit the problem of differentially private squared error linear regression. We observe that existing state-of-the-art methods are sensitive to the choice of hyperparameters -- including the ``clipping threshold'' that cannot be set optimally in a data-independent way. We give a new algorithm for private linear regression based on gradient boosting. We show that our method consistently improves over the previous state of the art when the clipping threshold is taken to be fixed without knowledge of the data, rather than optimized in a non-private way -- and that even when we optimize the hyperparameters of competitor algorithms non-privately, our algorithm is no worse and often better. In addition to a comprehensive set of experiments, we give theoretical insights to explain this behavior.

The Private Aggregation of Teacher Ensembles (PATE) is a machine learning framework that enables the creation of private models through the combination of multiple "teacher" models and a "student" model. The student model learns to predict an output based on the voting of the teachers, and the resulting model satisfies differential privacy. PATE has been shown to be effective in creating private models in semi-supervised settings or when protecting data labels is a priority. This paper explores whether the use of PATE can result in unfairness, and demonstrates that it can lead to accuracy disparities among groups of individuals. The paper also analyzes the algorithmic and data properties that contribute to these disproportionate impacts, why these aspects are affecting different groups disproportionately, and offers recommendations for mitigating these effects

Every day, the human brain processes an immense volume of visual information, relying on intricate neural mechanisms to perceive and interpret these stimuli. Recent breakthroughs in functional magnetic resonance imaging (fMRI) have enabled scientists to extract visual information from human brain activity patterns. In this study, we present an innovative method for decoding brain activity into meaningful images and captions, with a specific focus on brain captioning due to its enhanced flexibility as compared to brain decoding into images. Our approach takes advantage of cutting-edge image captioning models and incorporates a unique image reconstruction pipeline that utilizes latent diffusion models and depth estimation. We utilized the Natural Scenes Dataset, a comprehensive fMRI dataset from eight subjects who viewed images from the COCO dataset. We employed the Generative Image-to-text Transformer (GIT) as our backbone for captioning and propose a new image reconstruction pipeline based on latent diffusion models. The method involves training regularized linear regression models between brain activity and extracted features. Additionally, we incorporated depth maps from the ControlNet model to further guide the reconstruction process. We evaluate our methods using quantitative metrics for both generated captions and images. Our brain captioning approach outperforms existing methods, while our image reconstruction pipeline generates plausible images with improved spatial relationships. In conclusion, we demonstrate significant progress in brain decoding, showcasing the enormous potential of integrating vision and language to better understand human cognition. Our approach provides a flexible platform for future research, with potential applications in various fields, including neural art, style transfer, and portable devices.

The neural dynamics underlying brain activity are critical to understanding cognitive processes and mental disorders. However, current voxel-based whole-brain dimensionality reduction techniques fall short of capturing these dynamics, producing latent timeseries that inadequately relate to behavioral tasks. To address this issue, we introduce a novel approach to learning low-dimensional approximations of neural dynamics by using a sequential variational autoencoder (SVAE) that represents the latent dynamical system via a neural ordinary differential equation (NODE). Importantly, our method finds smooth dynamics that can predict cognitive processes with accuracy higher than classical methods. Our method also shows improved spatial localization to task-relevant brain regions and identifies well-known structures such as the motor homunculus from fMRI motor task recordings. We also find that non-linear projections to the latent space enhance performance for specific tasks, offering a promising direction for future research. We evaluate our approach on various task-fMRI datasets, including motor, working memory, and relational processing tasks, and demonstrate that it outperforms widely used dimensionality reduction techniques in how well the latent timeseries relates to behavioral sub-tasks, such as left-hand or right-hand tapping. Additionally, we replace the NODE with a recurrent neural network (RNN) and compare the two approaches to understand the importance of explicitly learning a dynamical system. Lastly, we analyze the robustness of the learned dynamical systems themselves and find that their fixed points are robust across seeds, highlighting our method's potential for the analysis of cognitive processes as dynamical systems.

In recent years, understanding the decision-making process of black-box models has become not only a legal requirement but also an additional way to assess their performance. However, the state of the art post-hoc interpretation approaches rely on synthetic data generation. This introduces uncertainty and can hurt the reliability of the interpretations. Furthermore, they tend to produce explanations that apply to only very few data points. This makes the explanations brittle and limited in scope. Finally, they provide scores that have no direct verifiable meaning. In this paper, we present BELLA, a deterministic model-agnostic post-hoc approach for explaining the individual predictions of regression black-box models. BELLA provides explanations in the form of a linear model trained in the feature space. Thus, its coefficients can be used directly to compute the predicted value from the feature values. Furthermore, BELLA maximizes the size of the neighborhood to which the linear model applies, so that the explanations are accurate, simple, general, and robust. BELLA can produce both factual and counterfactual explanations. Our user study confirms the importance of the desiderata we optimize, and our experiments show that BELLA outperforms the state-of-the-art approaches on these desiderata.