Neural Information Processing Systems http://nips.cc/

In this work we study loss functions for learning and evaluating probability distributions over large discrete domains. Unlike classification or regression where a wide variety of loss functions are used, in the distribution learning and density estimation literature, very few losses outside the dominant \emph{log loss} are applied. We aim to understand this fact, taking an axiomatic approach to the design of loss functions for distributions. We start by proposing a set of desirable criteria that any good loss function should satisfy. Intuitively, these criteria require that the loss function faithfully evaluates a candidate distribution, both in expectation and when estimated on a few samples.

Neural Information Processing Systems http://nips.cc/

In this work we study loss functions for learning and evaluating probability distributions over large discrete domains. Unlike classification or regression where a wide variety of loss functions are used, in the distribution learning and density estimation literature, very few losses outside the dominant \emph{log loss} are applied. We aim to understand this fact, taking an axiomatic approach to the design of loss functions for distributions. We start by proposing a set of desirable criteria that any good loss function should satisfy. Intuitively, these criteria require that the loss function faithfully evaluates a candidate distribution, both in expectation and when estimated on a few samples.

The Metropolis algorithm is one of the Markov chain Monte Carlo (MCMC) methods that realize sampling from the target probability distribution. In this paper, we are concerned with the sampling from the distribution in non-identifiable cases that involve models with Fisher information matrices that may fail to be invertible. The theoretical adjustment of the step size, which is the variance of the candidate distribution, is difficult for non-identifiable cases. In this study, to establish such a principle, the average acceptance rate, which is used as a guideline to optimize the step size in the MCMC method, was analytically derived in non-identifiable cases. The optimization principle for the step size was developed from the viewpoint of the average acceptance rate. In addition, we performed numerical experiments on some specific target distributions to verify the effectiveness of our theoretical results.

Multiple choice exams are widely used to assess candidates across a diverse range of domains and tasks. To moderate question quality, newly proposed questions often pass through pre-test evaluation stages before being deployed into real-world exams. Currently, this evaluation process is manually intensive, which can lead to time lags in the question development cycle. Streamlining this process via automation can significantly enhance efficiency, however, there's a current lack of datasets with adequate pre-test analysis information. In this paper we analyse a subset of the public Cambridge Multiple-Choice Questions Reading Database released by Cambridge University Press & Assessment; a multiple-choice comprehension dataset of questions at different target levels, with corresponding candidate selection distributions. We introduce the task of candidate distribution matching, propose several evaluation metrics for the task, and demonstrate that automatic systems trained on RACE++ can be leveraged as baselines for our task. We further demonstrate that these automatic systems can be used for practical pre-test evaluation tasks such as detecting underperforming distractors, where our detection systems can automatically identify poor distractors that few candidates select.

Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include the prominent generalized method of moments (GMM) which has recently gained attention in causal inference. GMM is a special case of the broader family of empirical likelihood estimators which are based on approximating a population distribution by means of minimizing a $\varphi$-divergence to an empirical distribution. However, the use of $\varphi$-divergences effectively limits the candidate distributions to reweightings of the data samples. We lift this long-standing limitation and provide a method of moments that goes beyond data reweighting. This is achieved by defining an empirical likelihood estimator based on maximum mean discrepancy which we term the kernel method of moments (KMM). We provide a variant of our estimator for conditional moment restrictions and show that it is asymptotically first-order optimal for such problems. Finally, we show that our method achieves competitive performance on several conditional moment restriction tasks.

Particle filtering is a common technique for six degree of freedom (6D) pose estimation due to its ability to tractably represent belief over object pose. However, the particle filter is prone to particle deprivation due to the high-dimensional nature of 6D pose. When particle deprivation occurs, it can cause mode collapse of the underlying belief distribution during importance sampling. If the region surrounding the true state suffers from mode collapse, recovering its belief is challenging since the area is no longer represented in the probability mass formed by the particles. Previous methods mitigate this problem by randomizing and resetting particles in the belief distribution, but determining the frequency of reinvigoration has relied on hand-tuning abstract heuristics. In this paper, we estimate the necessary reinvigoration rate at each time step by introducing a Counter-Hypothetical likelihood function, which is used alongside the standard likelihood. Inspired by the notions of plausibility and implausibility from Evidential Reasoning, the addition of our Counter-Hypothetical likelihood function assigns a level of doubt to each particle. The competing cumulative values of confidence and doubt across the particle set are used to estimate the level of failure within the filter, in order to determine the portion of particles to be reinvigorated. We demonstrate the effectiveness of our method on the rigid body object 6D pose tracking task.

Given a poorly documented neural network model, we take the perspective of a forensic investigator who wants to find out the model's data domain (e.g. whether on face images or traffic signs). Although existing methods such as membership inference and model inversion can be used to uncover some information about an unknown model, they still require knowledge of the data domain to start with. In this paper, we propose solving this problem by leveraging on comprehensive corpus such as ImageNet to select a meaningful distribution that is close to the original training distribution and leads to high performance in follow-up investigations. The corpus comprises two components, a large dataset of samples and meta information such as hierarchical structure and textual information on the samples. Our goal is to select a set of samples from the corpus for the given model. The core of our method is an objective function that considers two criteria on the selected samples: the model functional properties (derived from the dataset), and semantics (derived from the metadata). We also give an algorithm to efficiently search the large space of all possible subsets w.r.t. the objective function. Experimentation results show that the proposed method is effective. For example, cloning a given model (originally trained with CIFAR-10) by using Caltech 101 can achieve 45.5% accuracy. By using datasets selected by our method, the accuracy is improved to 72.0%.

Herding is a deterministic algorithm used to generate data points that can be regarded as random samples satisfying input moment conditions. The algorithm is based on the complex behavior of a high-dimensional dynamical system and is inspired by the maximum entropy principle of statistical inference. In this paper, we propose an extension of the herding algorithm, called entropic herding, which generates a sequence of distributions instead of points. Entropic herding is derived as the optimization of the target function obtained from the maximum entropy principle. Using the proposed entropic herding algorithm as a framework, we discuss a closer connection between herding and the maximum entropy principle. Specifically, we interpret the original herding algorithm as a tractable version of entropic herding, the ideal output distribution of which is mathematically represented. We further discuss how the complex behavior of the herding algorithm contributes to optimization. We argue that the proposed entropic herding algorithm extends the application of herding to probabilistic modeling. In contrast to original herding, entropic herding can generate a smooth distribution such that both efficient probability density calculation and sample generation become possible. To demonstrate the viability of these arguments in this study, numerical experiments were conducted, including a comparison with other conventional methods, on both synthetic and real data.