In this paper, we present a dual representation of the influence functions, whose computational complexity scales with dataset size rather than model size. Both analytically and experimentally, we show that this representation can be an efficient alternative to the original influence functions for estimating changes in parameters, model outputs and loss due to data point removal, when model size is large relative to dataset size, or when evaluating the original influence functions in parameter space is infeasible. The dual representation, however, is limited to linearizable models, which are models whose behavior can be approximated by their linearizations throughout training, and requires materializing a matrix, whose size grows with the product of model output dimension and dataset size.

We propose Lomax delegate racing (LDR) to explicitly model the mechanism of survival under competing risks and to interpret how the covariates accelerate or decelerate the time to event. LDR explains non-monotonic covariate effects by racing a potentially infinite number of sub-risks, and consequently relaxes the ubiquitous proportional-hazards assumption which may be too restrictive. Moreover, LDR is naturally able to model not only censoring, but also missing event times or event types. For inference, we develop a Gibbs sampler under data augmentation for moderately sized data, along with a stochastic gradient descent maximum a posteriori inference algorithm for big data applications. Illustrative experiments are provided on both synthetic and real datasets, and comparison with various benchmark algorithms for survival analysis with competing risks demonstrates distinguished performance of LDR.

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Inparticular, GANs generate samples of minor groups with low fidelity or even fail to generate such samples, exhibitingthemodecollapse[43].

We propose Lomax delegate racing (LDR) to explicitly model the mechanism of survival under competing risks and to interpret how the covariates accelerate or decelerate the time to event. LDR explains non-monotonic covariate effects by racing a potentially infinite number of sub-risks, and consequently relaxes the ubiquitous proportional-hazards assumption which may be too restrictive. Moreover, LDR is naturally able to model not only censoring, but also missing event times or event types. For inference, we develop a Gibbs sampler under data augmentation for moderately sized data, along with a stochastic gradient descent maximum a posteriori inference algorithm for big data applications. Illustrative experiments are provided on both synthetic and real datasets, and comparison with various benchmark algorithms for survival analysis with competing risks demonstrates distinguished performance of LDR.

Apart from modeling the time to event, in the presence of competing risks, it is also important to model the event type, or under which risk the event is likely to occur first. Though one can censor subjects with an occurrence of the event under a competing risk other than the risk of special interest, so that every survival model that can handle censoring is able to model competing risks, it is problematic to violate the principle of non-informative censoring [18, 19].

Whitening is a classical technique in unsupervised learning that can facilitate estimation tasks by standardizing data. An important application is the estimation of latent variable models via the decomposition of tensors built from high-order moments. In particular, whitening orthogonalizes the means of a spherical Gaussian mixture model (GMM), thereby making the corresponding moment tensor orthogonally decomposable, hence easier to decompose. However, in the large-dimensional regime (LDR) where data are high-dimensional and scarce, the standard whitening matrix built from the sample covariance becomes ineffective because the latter is spectrally distorted. Consequently, whitened means of a spherical GMM are no longer orthogonal. Using random matrix theory, we derive exact limits for their dot products, which are generally nonzero in the LDR. As our main contribution, we then construct a corrected whitening matrix that restores asymptotic orthogonality, allowing for performance gains in spherical GMM estimation.

Score-based diffusion models have achieved incredible performance in generating realistic images, audio, and video data. While these models produce high-quality samples with impressive details, they often introduce unrealistic artifacts, such as distorted fingers or hallucinated texts with no meaning. This paper focuses on textual hallucinations, where diffusion models correctly generate individual symbols but assemble them in a nonsensical manner. Through experimental probing, we consistently observe that such phenomenon is attributed it to the network's local generation bias. Denoising networks tend to produce outputs that rely heavily on highly correlated local regions, particularly when different dimensions of the data distribution are nearly pairwise independent. This behavior leads to a generation process that decomposes the global distribution into separate, independent distributions for each symbol, ultimately failing to capture the global structure, including underlying grammar. Intriguingly, this bias persists across various denoising network architectures including MLP and transformers which have the structure to model global dependency. These findings also provide insights into understanding other types of hallucinations, extending beyond text, as a result of implicit biases in the denoising models. Additionally, we theoretically analyze the training dynamics for a specific case involving a two-layer MLP learning parity points on a hypercube, offering an explanation of its underlying mechanism. Inspired by the diffusion process in physics (Sohl-Dickstein et al., 2015), diffusion models learn to generate samples from a specific data distribution by fitting its score function, gradually transforming pure Gaussian noise into desired samples. However, despite the impressively realistic details produced, diffusion models consistently exhibit artifacts in their outputs. One common issue is the generation of plausible low-level features or local details while failing to accurately model complex 3D objects or the underlying semantics (Borji, 2023; Liu et al., 2023).

When conducting large-scale studies that collect brain MR images from multiple facilities, the impact of differences in imaging equipment and protocols at each site cannot be ignored, and this domain gap has become a significant issue in recent years. In this study, we propose a new low-dimensional representation (LDR) acquisition method called style encoder adversarial domain adaptation (SE-ADA) to realize content-based image retrieval (CBIR) of brain MR images. SE-ADA reduces domain differences while preserving pathological features by separating domain-specific information from LDR and minimizing domain differences using adversarial learning. In evaluation experiments comparing SE-ADA with recent domain harmonization methods on eight public brain MR datasets (ADNI1/2/3, OASIS1/2/3/4, PPMI), SE-ADA effectively removed domain information while preserving key aspects of the original brain structure and demonstrated the highest disease search accuracy.