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We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered as a special case. Modern application areas make it increasingly challenging for Bayesians to attempt to model the true data-generating mechanism. For instance, when the object of interest is low dimensional, such as a mean or median, it is cumbersome to have to achieve this via a complete model for the whole data distribution. More importantly, there are settings where the parameter of interest does not directly index a family of density functions and thus the Bayesian approach to learning about such parameters is currently regarded as problematic. Our framework uses loss functions to connect information in the data to functionals of interest. The updating of beliefs then follows from a decision theoretic approach involving cumulative loss functions. Importantly, the procedure coincides with Bayesian updating when a true likelihood is known yet provides coherent subjective inference in much more general settings. Connections to other inference frameworks are highlighted.

Deep learning has been employed to prognostic and health management of automotive and aerospace with promising results. Literature in this area has revealed that most contributions regarding deep learning is largely focused on the model’s architecture. However, contributions regarding improvement of different aspects in deep learning, such as custom loss function for prognostic and health management are scarce. There is therefore an opportunity to improve upon the effectiveness of deep learning for the system’s prognostics and diagnostics without modifying the models’ architecture. To address this gap, the use of two different dynamically weighted loss functions, a newly proposed weighting mechanism and a focal loss function for prognostics and diagnostics task are investigated. A dynamically weighted loss function is expected to modify the learning process by augmenting the loss function with a weight value corresponding to the learning error of each data instance. The objective is to force deep learning models to focus on those instances where larger learning errors occur in order to improve their performance. The two loss functions used are evaluated using four popular deep learning architectures, namely, deep feedforward neural network, one-dimensional convolutional neural network, bidirectional gated recurrent unit and bidirectional long short-term memory on the commercial modular aero-propulsion system simulation data from NASA and air pressure system failure data for Scania trucks. Experimental results show that dynamically-weighted loss functions helps us achieve significant improvement for remaining useful life prediction and fault detection rate over non-weighted loss function predictions.

In the classical Poisson model, the distribution represents the number of events occurring within a given time or spatial interval. This study introduces new Bayesian methods for point estimation of the Poisson parameter, utilizing precautionary, entropy, and general entropy loss functions, particularly focusing on cases where the constants are c = 2 and 3. These methods are compared to traditional Bayesian estimators based on squared error and quadratic loss functions. A Monte Carlo simulation study was conducted to evaluate the performance of the proposed estimators, using mean squared error (MSE) as the primary criterion. The results demonstrate that the Bayesian approach, employing quadratic, entropy, and general entropy loss functions with c = 2, provided the most accurate estimates for smaller true parameter values ( 2 = 0.5, 1, or 2), yielding the lowest MSE. For moderately larger true parameter values (2=3, 5), the squared error and quadratic loss functions produced the minimum MSE across a range of sample sizes. For larger true parameter values (2 = 10, 20, 30, and 50), the precautionary loss function exhibited superior performance. These findings underscore the versatility and accuracy of different Bayesian loss functions for Poisson parameter estimation under varying conditions.

Physics-informed neural networks (PINNs) commonly use the mean squared error (MSE) as the loss function. However, this MSE is sensitive to high-residual regions and noise, often causing nonconvergence, overfitting, and loss imbalance during training. To address these challenges, we propose a Huber+ that combines the robustness of the Huber loss with a residual-driven weighting mechanism. The Huber loss transitions smoothly from the MSE for small residuals to the mean absolute error for large residuals, enhancing robustness and accuracy. Furthermore, the dynamic weighting mechanism adaptively adjusts loss weights on the basis of residual variations at each training point, effectively mitigating loss imbalance and enabling PINNs to focus on high-residual regions. To validate the effectiveness of the proposed method, we conduct comparative experiments, ablation studies, and noise sensitivity tests on the Allen–Cahn equation, the Burgers equation, and the Helmholtz equation. The experimental results show that the proposed strategy improves both accuracy and convergence speed.

Epithelial ovarian cancer (EOC) is a deadly cancer, and its prognosis has not been changed significantly during several decades. To seek new therapeutic targets for EOC, we performed an in vivo dropout screen in human tumor xenografts using a pooled shRNA library targeting thousands of druggable genes. Then, in follow-up studies, we performed a second screen using a genome-wide CRISPR/Cas9 library. These screens identified 10 high-confidence drug targets that included well-known oncogenes such as ERBB2 and RAF1, and novel oncogenes, notably KPNB1, which we investigated further. Genetic and pharmacological inhibition showed that KPNB1 exerts its antitumor effects through multiphase cell cycle arrest and apoptosis induction. Mechanistically, proteomic studies revealed that KPNB1 acts as a master regulator of cell cycle-related proteins, including p21, p27, and APC/C. Clinically, EOC patients with higher expression levels of KPNB1 showed earlier recurrence and worse prognosis than those with lower expression levels of KPNB1. Interestingly, ivermectin, a Food and Drug Administration-approved antiparasitic drug, showed KPNB1-dependent antitumor effects on EOC, serving as an alternative therapeutic toward EOC patients through drug repositioning. Last, we found that the combination of ivermectin and paclitaxel produces a stronger antitumor effect on EOC both in vitro and in vivo than either drug alone. Our studies have thus identified a combinatorial therapy for EOC, in addition to a plethora of potential drug targets.

This paper proposed a new family of loss function, as a generalization of weighted squared error loss function, aiming to construct more new loss functions. We proposed the definition of the generalized weighted squared error loss function and derived the Bayesian estimation and its posterior risk under the generalized weighted squared error loss function based on the definition. Moreover, some members of the family of the generalized weighted squared error loss function are discussed. The results show that the proposed generalized weighted squared error loss function contains some existing loss functions in special cases and can obviously be employed to generate more new ones. The expressions of Bayesian estimations and their posterior risks of Rayleigh distribution parameter under the squared error loss function, weighted squared-negative exponential error loss function and LINEX loss function are derived respectively. For ease of explanation, Monte Carlo simulation example and application example are provided, and the results are compared based on posterior risk.

N-methyl-D-aspartate receptors (NMDARs emerging from GRIN genes) are tetrameric receptors that form diverse channel compositions in neurons, typically consisting of two GluN1 subunits combined with two GluN2(A-D) subunits. During prenatal stages, the predominant channels are di-heteromers with two GluN1 and two GluN2B subunits due to the high abundance of GluN2B subunits. Postnatally, the expression of GluN2A subunits increases, giving rise to additional subtypes, including GluN2A-containing di-heteromers and tri-heteromers with GluN1, GluN2A, and GluN2B subunits. The latter  emerge as the major receptor subtype at mature synapses in the hippocampus. Despite extensive research on purely di-heteromeric receptors containing two identical GRIN variants, the impact of a single variant on the function of other channel forms, notably tri-heteromers, is lagging. In this study, we systematically investigated the effects of two de novo GRIN2B variants (G689C and G689S) in pure, mixed di- and tri-heteromers. Our findings reveal that incorporating a single variant in mixed di-heteromers or tri-heteromers exerts a dominant negative effect on glutamate potency, although ‘mixed’ channels show improved potency compared to pure variant-containing di-heteromers. We show that a single variant within a receptor complex does not impair the response of all receptor subtypes to the positive allosteric modulator pregnenolone-sulfate (PS), whereas spermine completely fails to potentiate tri-heteromers containing GluN2A and -2B-subunits. We examined PS on primary cultured hippocampal neurons transfected with the variants, and observed a positive impact over current amplitudes and synaptic activity. Together, our study supports previous observations showing that mixed di-heteromers exhibit improved glutamate potency and extend these findings towards the exploration of the effect of Loss-of-Function variants over tri-heteromers. Notably, we provide an initial and crucial demonstration of the beneficial effects of GRIN2B -relevant potentiators on tri-heteromers. Our results underscore the significance of studying how different variants affect distinct receptor subtypes, as these effects cannot be inferred solely from observations made on pure di-heteromers. Overall, this study contributes to ongoing efforts to understand the pathophysiology of GRINopathies and provides insights into potential treatment strategies.

Accurate segmentation in medical imaging requires loss functions that capture both regional overlap and boundary alignment. This study evaluates composite losses combining binary cross-entropy (BCE) and a boundary-based term under fixed and adaptive weighting schemes, using U-Net and SwinUNETR on the MM-WHS dataset. For U-Net, a small boundary contribution with adaptive weighting yielded the best results: Standard SoftAdapt (90/10 BCE + BoundaryDoU) achieved the highest Dice score ( ), surpassing both the baseline ( ) and fixed ratios. In contrast, SwinUNETR achieved its strongest performance with a fixed 70% BCE + 10% boundary ratio (0.919 ± 0.02). The result showed that combining a boundary-based loss term helps improve the segmentation accuracy. However, the performance gain is dependent on the architecture of the segmentation model; convolution-based U-Net benefited from the adaptive loss weighting scheme, whereas Transformer-based SwinUNETR without strong inductive bias did not benefit from increased influence of the boundary loss term.

CRISPR-Cas9 gene editing has transformed our ability to rapidly interrogate the functional impact of somatic mutations in human cancers. Droplet-based technology enables the analysis of Cas9-introduced gene edits in thousands of single cells. Using this technology, we analyze Ba/F3 cells engineered to express single or multiplexed loss-of-function mutations recurrent in chronic lymphocytic leukemia. Our approach reliably quantifies mutational co-occurrences, zygosity status, and the occurrence of Cas9 edits at single-cell resolution.

Support vector data description (SVDD) is widely regarded as an effective technique for addressing anomaly detection problems. However, its performance can significantly deteriorate when the training data are affected by outliers or mislabeled observations. This study introduces a universal truncated loss function framework into the SVDD model to enhance its robustness and employs the fast alternating direction method of multipliers (ADMM) algorithm to solve various truncated loss functions. Moreover, the convergence of the fast ADMM algorithm is analyzed theoretically. Within this framework, we developed the truncated generalized ramp, truncated binary cross entropy, and truncated linear exponential loss functions for SVDD. We conducted extensive experiments on synthetic and real-world datasets to validate the effectiveness of these three SVDD models in handling data with different noise levels, demonstrating their superior robustness and generalization capabilities compared to other SVDD models.