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The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal likelihoods depends on the prior choice. For model selection, even diffuse priors can be actually very informative, unlike for the parameter estimation problem. Furthermore, when the prior is improper, the marginal likelihood of the corresponding model is undetermined. In this work, we discuss the issue of prior sensitivity of the marginal likelihood and its role in model selection. We also comment on the use of uninformative priors, which are very common choices in practice. Several practical suggestions are discussed and many possible solutions, proposed in the literature, to design objective priors for model selection are described. Some of them also allow the use of improper priors. The connection between the marginal likelihood approach and the well-known information criteria is also presented. We describe the main issues and possible solutions by illustrative numerical examples, providing also some related code. One of them involving a real-world application on exoplanet detection.

Estimating the distance of objects is a safety-critical task for autonomous driving. Focusing on short-range objects, existing methods and datasets neglect the equally important long-range objects. In this paper, we introduce a challenging and under-explored task, which we refer to as Long-Range Distance Estimation, as well as two datasets to validate new methods developed for this task. We then proposeR4D, the first framework to accurately estimate the distance of long-range objects by using references with known distances in the scene. Drawing inspiration from human perception, R4D builds a graph by connecting a target object to all references. An edge in the graph encodes the relative distance information between a pair of target and reference objects. An attention module is then used to weigh the importance of reference objects and combine them into one target object distance prediction. Experiments on the two proposed datasets demonstrate the effectiveness and robustness of R4D by showing significant improvements compared to existing baselines. We are looking to make the proposed dataset, Waymo OpenDataset - Long-Range Labels, available publicly at waymo.com/open/download.

The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation. Here, we introduce an alternative scheme based on integrating an ordinary differential equation that describes the flow of probability. Unlike the stochastic dynamics, this equation deterministically pushes samples from the initial density onto samples from the solution at any later time. The method has the advantage of giving direct access to quantities that are challenging to estimate only given samples from the solution, such as the probability current, the density itself, and its entropy. The probability flow equation depends on the gradient of the logarithm of the solution (its "score"), and so is a-priori unknown. To resolve this dependence, we model the score with a deep neural network that is learned on-the-fly by propagating a set of particles according to the instantaneous probability current. Our approach is based on recent advances in score-based diffusion for generative modeling, with the important difference that the training procedure is self-contained and does not require samples from the target density to be available beforehand. To demonstrate the validity of the approach, we consider several examples from the physics of interacting particle systems; we find that the method scales well to high-dimensional systems, and accurately matches available analytical solutions and moments computed via Monte-Carlo.

State-of-the-art Named Entity Recognition(NER) models rely heavily on large amountsof fully annotated training data. However, ac-cessible data are often incompletely annotatedsince the annotators usually lack comprehen-sive knowledge in the target domain. Normallythe unannotated tokens are regarded as non-entities by default, while we underline thatthese tokens could either be non-entities orpart of any entity. Here, we study NER mod-eling with incomplete annotated data whereonly a fraction of the named entities are la-beled, and the unlabeled tokens are equiva-lently multi-labeled by every possible label.Taking multi-labeled tokens into account, thenumerous possible paths can distract the train-ing model from the gold path (ground truthlabel sequence), and thus hinders the learn-ing ability. In this paper, we propose AdaK-NER, named the adaptive top-Kapproach, tohelp the model focus on a smaller feasible re-gion where the gold path is more likely to belocated. We demonstrate the superiority ofour approach through extensive experimentson both English and Chinese datasets, aver-agely improving 2% in F-score on the CoNLL-2003 and over 10% on two Chinese datasetscompared with the prior state-of-the-art works.

Two of the most significant challenges in uncertainty quantification pertain to the high computational cost for simulating complex physical models and the high dimension of the random inputs. In applications of practical interest, both of these problems are encountered, and standard methods either fail or are not feasible. To overcome the current limitations, we present a generalized formulation of a Bayesian multi-fidelity Monte-Carlo (BMFMC) framework that can exploit lower-fidelity model versions in a small data regime. The goal of our analysis is an efficient and accurate estimation of the complete probabilistic response for high-fidelity models. BMFMC circumvents the curse of dimensionality by learning the relationship between the outputs of a reference high-fidelity model and potentially several lower-fidelity models. While the continuous formulation is mathematically exact and independent of the low-fidelity model's accuracy, we address challenges associated with the small data regime (i.e., only a small number of 50 to 300 high-fidelity model runs can be performed). Specifically, we complement the formulation with a set of informative input features at no extra cost. Despite the inaccurate and noisy information that some low-fidelity models provide, we demonstrate that accurate and certifiable estimates for the quantities of interest can be obtained for uncertainty quantification problems in high stochastic dimensions, with significantly fewer high-fidelity model runs than state-of-the-art methods for uncertainty quantification. We illustrate our approach by applying it to challenging numerical examples such as Navier-Stokes flow simulations and fluid-structure interaction problems.

Landscape-aware algorithm selection approaches have so far mostly been relying on landscape feature extraction as a preprocessing step, independent of the execution of optimization algorithms in the portfolio. This introduces a significant overhead in computational cost for many practical applications, as features are extracted and computed via sampling and evaluating the problem instance at hand, similarly to what the optimization algorithm would perform anyway within its search trajectory. As suggested in Jankovic et al. (EvoAPPs 2021), trajectory-based algorithm selection circumvents the problem of costly feature extraction by computing landscape features from points that a solver sampled and evaluated during the optimization process. Features computed in this manner are used to train algorithm performance regression models, upon which a per-run algorithm selector is then built. In this work, we apply the trajectory-based approach onto a portfolio of five algorithms. We study the quality and accuracy of performance regression and algorithm selection models in the scenario of predicting different algorithm performances after a fixed budget of function evaluations. We rely on landscape features of the problem instance computed using one portion of the aforementioned budget of the same function evaluations. Moreover, we consider the possibility of switching between the solvers once, which requires them to be warm-started, i.e. when we switch, the second solver continues the optimization process already being initialized appropriately by making use of the information collected by the first solver. In this new context, we show promising performance of the trajectory-based per-run algorithm selection with warm-starting.

In machine learning, we traditionally evaluate the performance of a single model, averaged over a collection of test inputs. In this work, we propose a new approach: we measure the performance of a collection of models when evaluated on a $\textit{single input point}$. Specifically, we study a point's $\textit{profile}$: the relationship between models' average performance on the test distribution and their pointwise performance on this individual point. We find that profiles can yield new insights into the structure of both models and data -- in and out-of-distribution. For example, we empirically show that real data distributions consist of points with qualitatively different profiles. On one hand, there are "compatible" points with strong correlation between the pointwise and average performance. On the other hand, there are points with weak and even $\textit{negative}$ correlation: cases where improving overall model accuracy actually $\textit{hurts}$ performance on these inputs. We prove that these experimental observations are inconsistent with the predictions of several simplified models of learning proposed in prior work. As an application, we use profiles to construct a dataset we call CIFAR-10-NEG: a subset of CINIC-10 such that for standard models, accuracy on CIFAR-10-NEG is $\textit{negatively correlated}$ with accuracy on CIFAR-10 test. This illustrates, for the first time, an OOD dataset that completely inverts "accuracy-on-the-line" (Miller, Taori, Raghunathan, Sagawa, Koh, Shankar, Liang, Carmon, and Schmidt 2021)

Link prediction on knowledge graphs (KGs) is a key research topic. Previous work mainly focused on binary relations, paying less attention to higher-arity relations although they are ubiquitous in real-world KGs. This paper considers link prediction upon n-ary relational facts and proposes a graph-based approach to this task. The key to our approach is to represent the n-ary structure of a fact as a small heterogeneous graph, and model this graph with edge-biased fully-connected attention. The fully-connected attention captures universal inter-vertex interactions, while with edge-aware attentive biases to particularly encode the graph structure and its heterogeneity. In this fashion, our approach fully models global and local dependencies in each n-ary fact, and hence can more effectively capture associations therein. Extensive evaluation verifies the effectiveness and superiority of our approach. It performs substantially and consistently better than current state-of-the-art across a variety of n-ary relational benchmarks. Our code is publicly available.

A key requirement for the success of supervised deep learning is a large labeled dataset - a condition that is difficult to meet in medical image analysis. Self-supervised learning (SSL) can help in this regard by providing a strategy to pre-train a neural network with unlabeled data, followed by fine-tuning for a downstream task with limited annotations. Contrastive learning, a particular variant of SSL, is a powerful technique for learning image-level representations. In this work, we propose strategies for extending the contrastive learning framework for segmentation of volumetric medical images in the semi-supervised setting with limited annotations, by leveraging domain-specific and problem-specific cues. Specifically, we propose (1) novel contrasting strategies that leverage structural similarity across volumetric medical images (domain-specific cue) and (2) a local version of the contrastive loss to learn distinctive representations of local regions that are useful for per-pixel segmentation (problem-specific cue). We carry out an extensive evaluation on three Magnetic Resonance Imaging (MRI) datasets. In the limited annotation setting, the proposed method yields substantial improvements compared to other self-supervision and semi-supervised learning techniques. When combined with a simple data augmentation technique, the proposed method reaches within 8% of benchmark performance using only two labeled MRI volumes for training, corresponding to only 4% (for ACDC) of the training data used to train the benchmark.

We consider the task of weakly supervised one-shot detection. In this task, we attempt to perform a detection task over a set of unseen classes, when training only using weak binary labels that indicate the existence of a class instance in a given example. The model is conditioned on a single exemplar of an unseen class and a target example that may or may not contain an instance of the same class as the exemplar. A similarity map is computed by using a Siamese neural network to map the exemplar and regions of the target example to a latent representation space and then computing cosine similarity scores between representations. An attention mechanism weights different regions in the target example, and enables learning of the one-shot detection task using the weaker labels alone. The model can be applied to detection tasks from different domains, including computer vision object detection. We evaluate our attention Siamese networks on a one-shot detection task from the audio domain, where it detects audio keywords in spoken utterances. Our model considerably outperforms a baseline approach and yields a 42.6% average precision for detection across 10 unseen classes. Moreover, architectural developments from computer vision object detection models such as a region proposal network can be incorporated into the model architecture, and results show that performance is expected to improve by doing so.