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Survival analysis is a crucial semi-supervised task in machine learning with numerous real-world applications, particularly in healthcare. Currently, the most common approach to survival analysis is based on Cox's partial likelihood, which can be interpreted as a ranking model optimized on a lower bound of the concordance index. This relation between ranking models and Cox's partial likelihood considers only pairwise comparisons. Recent work has developed differentiable sorting methods which relax this pairwise independence assumption, enabling the ranking of sets of samples. However, current differentiable sorting methods cannot account for censoring, a key factor in many real-world datasets. To address this limitation, we propose a novel method called Diffsurv. We extend differentiable sorting methods to handle censored tasks by predicting matrices of possible permutations that take into account the label uncertainty introduced by censored samples. We contrast this approach with methods derived from partial likelihood and ranking losses. Our experiments show that Diffsurv outperforms established baselines in various simulated and real-world risk prediction scenarios. Additionally, we demonstrate the benefits of the algorithmic supervision enabled by Diffsurv by presenting a novel method for top-k risk prediction that outperforms current methods.

Modern advanced manufacturing and advanced materials design often require searches of relatively high-dimensional process control parameter spaces for settings that result in optimal structure, property, and performance parameters. The mapping from the former to the latter must be determined from noisy experiments or from expensive simulations. We abstract this problem to a mathematical framework in which an unknown function from a control space to a design space must be ascertained by means of expensive noisy measurements, which locate optimal control settings generating desired design features within specified tolerances, with quantified uncertainty. We describe targeted adaptive design (TAD), a new algorithm that performs this sampling task efficiently. TAD creates a Gaussian process surrogate model of the unknown mapping at each iterative stage, proposing a new batch of control settings to sample experimentally and optimizing the updated log-predictive likelihood of the target design. TAD either stops upon locating a solution with uncertainties that fit inside the tolerance box or uses a measure of expected future information to determine that the search space has been exhausted with no solution. TAD thus embodies the exploration-exploitation tension in a manner that recalls, but is essentially different from, Bayesian optimization and optimal experimental design.

While massive valuable deep models trained on large-scale data have been released to facilitate the artificial intelligence community, they may encounter attacks in deployment which leads to privacy leakage of training data. In this work, we propose a learning approach termed differentially private data-free distillation (DPDFD) for model conversion that can convert a pretrained model (teacher) into its privacy-preserving counterpart (student) via an intermediate generator without access to training data. The learning collaborates three parties in a unified way. First, massive synthetic data are generated with the generator. Then, they are fed into the teacher and student to compute differentially private gradients by normalizing the gradients and adding noise before performing descent. Finally, the student is updated with these differentially private gradients and the generator is updated by taking the student as a fixed discriminator in an alternate manner. In addition to a privacy-preserving student, the generator can generate synthetic data in a differentially private way for other downstream tasks. We theoretically prove that our approach can guarantee differential privacy and well convergence. Extensive experiments clearly demonstrate that our approach significantly outperform other differentially private generative approaches.

Learning multi-view data is an emerging problem in machine learning research, and nonnegative matrix factorization (NMF) is a popular dimensionality-reduction method for integrating information from multiple views. These views often provide not only consensus but also complementary information. However, most multi-view NMF algorithms assign equal weight to each view or tune the weight via line search empirically, which can be infeasible without any prior knowledge of the views or computationally expensive. In this paper, we propose a weighted multi-view NMF (WM-NMF) algorithm. In particular, we aim to address the critical technical gap, which is to learn both view-specific weight and observation-specific reconstruction weight to quantify each view's information content. The introduced weighting scheme can alleviate unnecessary views' adverse effects and enlarge the positive effects of the important views by assigning smaller and larger weights, respectively. Experimental results confirm the effectiveness and advantages of the proposed algorithm in terms of achieving better clustering performance and dealing with the noisy data compared to the existing algorithms.

Functional data is a powerful tool for capturing and analyzing complex patterns and relationships in a variety of fields, allowing for more precise modeling, visualization, and decision-making. For example, in healthcare, functional data such as medical images can help doctors make more accurate diagnoses and develop more effective treatment plans. However, understanding the causal relationships between functional predictors and time-to-event outcomes remains a challenge. To address this, we propose a functional causal framework including a functional accelerated failure time (FAFT) model and three causal approaches. The regression adjustment approach is based on conditional FAFT with subsequent confounding marginalization, while the functional-inverse-probability-weighting approach is based on marginal FAFT with well-defined functional propensity scores. The double robust approach combines the strengths of both methods and achieves a balance condition through the weighted residuals between imputed observations and regression adjustment outcomes. Our approach can accurately estimate causality, predict outcomes, and is robust to different censoring rates. We demonstrate the power of our framework with simulations and real-world data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. Our findings provide more precise subregions of the hippocampus that align with medical research, highlighting the power of this work for improving healthcare outcomes.

Many social events and policy interventions generate treatment effects that persistently spill over into neighboring areas, causing interference in both time and space. In this paper, we propose a design-based framework to identify and estimate these spillover effects in panel data, when temporal and spatial interference intertwine with each other in complex ways that are unknown to researchers. Our framework defines estimands that enable researchers to measure the influence of each type of interference, and we propose estimators that are consistent and asymptotically normal under the assumption of sequential ignorability and mild regularity conditions. We show that conventional methods in panel data analysis, such as the difference-in-differences (DID) estimator or fixed effects models, can lead to significant biases in such scenarios. We test the method's performance on both simulated datasets and the replication of an empirical study from political science.

In this paper, we study the stochastic linear bandit problem under the additional requirements of differential privacy, robustness and batched observations. In particular, we assume an adversary randomly chooses a constant fraction of the observed rewards in each batch, replacing them with arbitrary numbers. We present differentially private and robust variants of the arm elimination algorithm using logarithmic batch queries under two privacy models and provide regret bounds in both settings. In the first model, every reward in each round is reported by a potentially different client, which reduces to standard local differential privacy (LDP). In the second model, every action is "owned" by a different client, who may aggregate the rewards over multiple queries and privatize the aggregate response instead. To the best of our knowledge, our algorithms are the first simultaneously providing differential privacy and adversarial robustness in the stochastic linear bandits problem.

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.

We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.

In semi-supervised domain adaptation, a few labeled samples per class in the target domain guide features of the remaining target samples to aggregate around them. However, the trained model cannot produce a highly discriminative feature representation for the target domain because the training data is dominated by labeled samples from the source domain. This could lead to disconnection between the labeled and unlabeled target samples as well as misalignment between unlabeled target samples and the source domain. In this paper, we propose a novel approach called Cross-domain Adaptive Clustering to address this problem. To achieve both inter-domain and intra-domain adaptation, we first introduce an adversarial adaptive clustering loss to group features of unlabeled target data into clusters and perform cluster-wise feature alignment across the source and target domains. We further apply pseudo labeling to unlabeled samples in the target domain and retain pseudo-labels with high confidence. Pseudo labeling expands the number of ``labeled" samples in each class in the target domain, and thus produces a more robust and powerful cluster core for each class to facilitate adversarial learning. Extensive experiments on benchmark datasets, including DomainNet, Office-Home and Office, demonstrate that our proposed approach achieves the state-of-the-art performance in semi-supervised domain adaptation.