Uncertainty estimation (UE), as an effective means of quantifying predictive uncertainty, is crucial for safe and reliable decision-making, especially in high-risk scenarios. Existing UE schemes usually assume that there are completely-labeled samples to support fully-supervised learning. In practice, however, many UE tasks often have no sufficiently-labeled data to use, such as the Multiple Instance Learning (MIL) with only weak instance annotations. To bridge this gap, this paper, for the first time, addresses the weakly-supervised issue of Multi-Instance UE (MIUE) and proposes a new baseline scheme, Multi-Instance Residual Evidential Learning (MIREL). Particularly, at the fine-grained instance UE with only weak supervision, we derive a multi-instance residual operator through the Fundamental Theorem of Symmetric Functions. On this operator derivation, we further propose MIREL to jointly model the high-order predictive distribution at bag and instance levels for MIUE. Extensive experiments empirically demonstrate that our MIREL not only could often make existing MIL networks perform better in MIUE, but also could surpass representative UE methods by large margins, especially in instance-level UE tasks. Our source code is available at https://github.com/liupei101/MIREL.

Cross-domain offline reinforcement learning leverages source domain data with diverse transition dynamics to alleviate the data requirement for the target domain. However, simply merging the data of two domains leads to performance degradation due to the dynamics mismatch. Existing methods address this problem by measuring the dynamics gap via domain classifiers while relying on the assumptions of the transferability of paired domains. In this paper, we propose a novel representation-based approach to measure the domain gap, where the representation is learned through a contrastive objective by sampling transitions from different domains. We show that such an objective recovers the mutual-information gap of transition functions in two domains without suffering from the unbounded issue of the dynamics gap in handling significantly different domains. Based on the representations, we introduce a data filtering algorithm that selectively shares transitions from the source domain according to the contrastive score functions. Empirical results on various tasks demonstrate that our method achieves superior performance, using only 10% of the target data to achieve 89.2% of the performance on 100% target dataset with state-of-the-art methods.

Suicide is a prominent issue in society. Unfortunately, many people at risk for suicide do not receive the support required. Barriers to people receiving support include social stigma and lack of access to mental health care. With the popularity of social media, people have turned to online forums, such as Reddit to express their feelings and seek support. This provides the opportunity to support people with the aid of artificial intelligence. Social media posts can be classified, using text classification, to help connect people with professional help. However, these systems fail to account for the inherent uncertainty in classifying mental health conditions. Unlike other areas of healthcare, mental health conditions have no objective measurements of disease often relying on expert opinion. Thus when formulating deep learning problems involving mental health, using hard, binary labels does not accurately represent the true nature of the data. In these settings, where human experts may disagree, fuzzy or soft labels may be more appropriate. The current work introduces a novel label smoothing method which we use to capture any uncertainty within the data. We test our approach on a five-label multi-class classification problem. We show, our semi-supervised deep label smoothing method improves classification accuracy above the existing state of the art. Where existing research reports an accuracy of 43\% on the Reddit C-SSRS dataset, using empirical experiments to evaluate our novel label smoothing method, we improve upon this existing benchmark to 52\%. These improvements in model performance have the potential to better support those experiencing mental distress. Future work should explore the use of probabilistic methods in both natural language processing and quantifying contributions of both epistemic and aleatoric uncertainty in noisy datasets.

We introduce a novel multi-armed bandit framework, where each arm is associated with a fixed unknown credal set over the space of outcomes (which can be richer than just the reward). The arm-to-credal-set correspondence comes from a known class of hypotheses. We then define a notion of regret corresponding to the lower prevision defined by these credal sets. Equivalently, the setting can be regarded as a two-player zero-sum game, where, on each round, the agent chooses an arm and the adversary chooses the distribution over outcomes from a set of options associated with this arm. The regret is defined with respect to the value of game. For certain natural hypothesis classes, loosely analgous to stochastic linear bandits (which are a special case of the resulting setting), we propose an algorithm and prove a corresponding upper bound on regret. We also prove lower bounds on regret for particular special cases.

There have been many applications of deep neural networks to detector calibrations and a growing number of studies that propose deep generative models as automated fast detector simulators. We show that these two tasks can be unified by using maximum likelihood estimation (MLE) from conditional generative models for energy regression. Unlike direct regression techniques, the MLE approach is prior-independent and non-Gaussian resolutions can be determined from the shape of the likelihood near the maximum. Using an ATLAS-like calorimeter simulation, we demonstrate this concept in the context of calorimeter energy calibration.

The Twelfth International Conference on Learning Representations (ICLR) is taking place this week in Vienna, Austria. During the opening of the conference, the outstanding paper award winners, and honourable mentions, were announced. The conference organisers also introduced a new award for this year: the test of time award. This award honours a paper from 2013/2014 that the programme chairs judge to have had a lasting impact. Abstract: How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets?

Numerous applications in biology, statistics, science, and engineering require generating samples from high-dimensional probability distributions. In recent years, the Hamiltonian Monte Carlo (HMC) method has emerged as a state-of-the-art Markov chain Monte Carlo technique, exploiting the shape of such high-dimensional target distributions to efficiently generate samples. Despite its impressive empirical success and increasing popularity, its wide-scale adoption remains limited due to the high computational cost of gradient calculation. Moreover, applying this method is impossible when the gradient of the posterior cannot be computed (for example, with black-box simulators). To overcome these challenges, we propose a novel two-stage Hamiltonian Monte Carlo algorithm with a surrogate model. In this multi-fidelity algorithm, the acceptance probability is computed in the first stage via a standard HMC proposal using an inexpensive differentiable surrogate model, and if the proposal is accepted, the posterior is evaluated in the second stage using the high-fidelity (HF) numerical solver. Splitting the standard HMC algorithm into these two stages allows for approximating the gradient of the posterior efficiently, while producing accurate posterior samples by using HF numerical solvers in the second stage. We demonstrate the effectiveness of this algorithm for a range of problems, including linear and nonlinear Bayesian inverse problems with in-silico data and experimental data. The proposed algorithm is shown to seamlessly integrate with various low-fidelity and HF models, priors, and datasets. Remarkably, our proposed method outperforms the traditional HMC algorithm in both computational and statistical efficiency by several orders of magnitude, all while retaining or improving the accuracy in computed posterior statistics.

We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The notion of data separability is not needed, which is in contrast to the classical set up of multi-class logistic regression in which each data sample belongs to one class. We also provide a general and constructive estimate of the convergence rate to the maximum likelihood estimate when gradient descent is used as the optimizer. Our estimate involves bounding the condition number of the Hessian of the maximum likelihood function. The approaches used in this article rely on a simple operator-theoretic framework.

Permutation invariance is among the most common symmetry that can be exploited to simplify complex problems in machine learning (ML). There has been a tremendous surge of research activities in building permutation invariant ML architectures. However, less attention is given to: (1) how to statistically test for permutation invariance of coordinates in a random vector where the dimension is allowed to grow with the sample size; (2) how to leverage permutation invariance in estimation problems and how does it help reduce dimensions. In this paper, we take a step back and examine these questions in several fundamental problems: (i) testing the assumption of permutation invariance of multivariate distributions; (ii) estimating permutation invariant densities; (iii) analyzing the metric entropy of permutation invariant function classes and compare them with their counterparts without imposing permutation invariance; (iv) deriving an embedding of permutation invariant reproducing kernel Hilbert spaces for efficient computation. In particular, our methods for (i) and (iv) are based on a sorting trick and (ii) is based on an averaging trick. These tricks substantially simplify the exploitation of permutation invariance.

Instrumental variables (IVs) are a popular and powerful tool for estimating causal effects in the presence of unobserved confounding. However, classical approaches rely on strong assumptions such as the $\textit{exclusion criterion}$, which states that instrumental effects must be entirely mediated by treatments. This assumption often fails in practice. When IV methods are improperly applied to data that do not meet the exclusion criterion, estimated causal effects may be badly biased. In this work, we propose a novel solution that provides $\textit{partial}$ identification in linear systems given a set of $\textit{leaky instruments}$, which are allowed to violate the exclusion criterion to some limited degree. We derive a convex optimization objective that provides provably sharp bounds on the average treatment effect under some common forms of information leakage, and implement inference procedures to quantify the uncertainty of resulting estimates. We demonstrate our method in a set of experiments with simulated data, where it performs favorably against the state of the art. An accompanying $\texttt{R}$ package, $\texttt{leakyIV}$, is available from $\texttt{CRAN}$.