Related papers: Edgeworth Expansion for Semi-hard Triplet Loss

We consider sums of independent identically distributed random variables whose distributions have $d+1$ atoms. Such distributions never admit an Edgeworth expansion of order $d$ but we show that for almost all parameters the Edgeworth…

Metric learning aims to learn a distance metric such that semantically similar instances are pulled together while dissimilar instances are pushed away. Many existing methods consider maximizing or at least constraining a distance margin in…

In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and…

The optimization foundations of deep linear networks have recently received significant attention. However, due to their inherent non-convexity and hierarchical structure, analyzing the loss functions of deep linear networks remains a…

We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Second order Edgeworth type expansions for transition densities are proved. The paper differs from recent results in two respects. We allow…

We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…

Deep metric learning has yielded impressive results in tasks such as clustering and image retrieval by leveraging neural networks to obtain highly discriminative feature embeddings, which can be used to group samples into different classes.…

We establish the validity of the empirical Edgeworth expansion (EE) for a studentized trimmed mean, under the sole condition that the underlying distribution function of the observations satisfies a local smoothness condition near the two…

Deep embeddings answer one simple question: How similar are two images? Learning these embeddings is the bedrock of verification, zero-shot learning, and visual search. The most prominent approaches optimize a deep convolutional network…

Deep metric learning has attracted much attention in recent years, due to seamlessly combining the distance metric learning and deep neural network. Many endeavors are devoted to design different pair-based angular loss functions, which…

For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…

Traditional loss functions, including cross-entropy, contrastive, triplet, and su pervised contrastive losses, used for fine-tuning pre-trained language models such as BERT, operate only within local neighborhoods and fail to account for…

Given n observations, we study the consistency of a batch of k new observations, in terms of their distribution function. We propose a non-parametric, non-likelihood test based on Edgeworth expansion of the distribution function. The…

In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…

We consider the transmission eigenvalue problem for an impenetrable obstacle with Dirichlet boundary condition surrounded by a thin layer of non-absorbing inhomogeneous material. We derive a rigorous asymptotic expansion for the first…

The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…

In this paper, we derive a valid Edgeworth expansions for the Bessel corrected empirical variance when data are generated by a strongly mixing process whose distribution can be arbitrarily. The constraint of strongly mixing process makes…

Edge detection (ED) remains a fundamental task in computer vision, yet its performance is often hindered by the ambiguous nature of non-edge pixels near object boundaries. The widely adopted Weighted Binary Cross-Entropy (WBCE) loss treats…

Sensitivity analysis is important to assess the impact of unmeasured confounding in causal inference from observational studies. The marginal sensitivity model (MSM) provides a useful approach in quantifying the influence of unmeasured…

By transferring knowledge learned from seen/previous tasks, meta learning aims to generalize well to unseen/future tasks. Existing meta-learning approaches have shown promising empirical performance on various multiclass classification…