Data harmonization is the process by which an equivalence is developed between two variables measuring a common trait. Our problem is motivated by dementia research in which multiple tests are used in practice to measure the same underlying cognitive ability such as language or memory. We connect this statistical problem to mixing distribution estimation. We introduce and study a non-parametric latent trait model, develop a method which enforces uniqueness of the regularized maximum likelihood estimator, show how a nonparametric EM algorithm will converge weakly to its maximizer, and additionally propose a faster algorithm for learning a discretized approximation of the latent distribution. Furthermore, we develop methods to assess goodness of fit for the mixing likelihood which is an area neglected in most mixing distribution estimation problems. We apply our method to the National Alzheimer's Coordination Center Uniform Data Set and show that we can use our method to convert between score measurements and account for the measurement error. We show that this method outperforms standard techniques commonly used in dementia research. Full code is available at //github.com/SteveJWR/Data-Harmonization-Nonparametric.
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We propose a theoretical study of two realistic estimators of conditional distribution functions and conditional quantiles using random forests. The estimation process uses the bootstrap samples generated from the original dataset when constructing the forest. Bootstrap samples are reused to define the first estimator, while the second requires only the original sample, once the forest has been built. We prove that both proposed estimators of the conditional distribution functions are consistent uniformly a.s. To the best of our knowledge, it is the first proof of consistency including the bootstrap part. We also illustrate the estimation procedures on a numerical example.
While post-training quantization receives popularity mostly due to its evasion in accessing the original complete training dataset, its poor performance also stems from this limitation. To alleviate this limitation, in this paper, we leverage the synthetic data introduced by zero-shot quantization with calibration dataset and we propose a fine-grained data distribution alignment (FDDA) method to boost the performance of post-training quantization. The method is based on two important properties of batch normalization statistics (BNS) we observed in deep layers of the trained network, i.e., inter-class separation and intra-class incohesion. To preserve this fine-grained distribution information: 1) We calculate the per-class BNS of the calibration dataset as the BNS centers of each class and propose a BNS-centralized loss to force the synthetic data distributions of different classes to be close to their own centers. 2) We add Gaussian noise into the centers to imitate the incohesion and propose a BNS-distorted loss to force the synthetic data distribution of the same class to be close to the distorted centers. By introducing these two fine-grained losses, our method shows the state-of-the-art performance on ImageNet, especially when the first and last layers are quantized to low-bit as well. Our project is available at //github.com/zysxmu/FDDA.
Reconstructing the 3D pose of a person in metric scale from a single view image is a geometrically ill-posed problem. For example, we can not measure the exact distance of a person to the camera from a single view image without additional scene assumptions (e.g., known height). Existing learning based approaches circumvent this issue by reconstructing the 3D pose up to scale. However, there are many applications such as virtual telepresence, robotics, and augmented reality that require metric scale reconstruction. In this paper, we show that audio signals recorded along with an image, provide complementary information to reconstruct the metric 3D pose of the person. The key insight is that as the audio signals traverse across the 3D space, their interactions with the body provide metric information about the body's pose. Based on this insight, we introduce a time-invariant transfer function called pose kernel -- the impulse response of audio signals induced by the body pose. The main properties of the pose kernel are that (1) its envelope highly correlates with 3D pose, (2) the time response corresponds to arrival time, indicating the metric distance to the microphone, and (3) it is invariant to changes in the scene geometry configurations. Therefore, it is readily generalizable to unseen scenes. We design a multi-stage 3D CNN that fuses audio and visual signals and learns to reconstruct 3D pose in a metric scale. We show that our multi-modal method produces accurate metric reconstruction in real world scenes, which is not possible with state-of-the-art lifting approaches including parametric mesh regression and depth regression.
We provide explicit bounds on the number of sample points required to estimate tangent spaces and intrinsic dimensions of (smooth, compact) Euclidean submanifolds via local principal component analysis. Our approach directly estimates covariance matrices locally, which simultaneously allows estimating both the tangent spaces and the intrinsic dimension of a manifold. The key arguments involve a matrix concentration inequality, a Wasserstein bound for flattening a manifold, and a Lipschitz relation for the covariance matrix with respect to the Wasserstein distance.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale datasets. Among the possible strategies to alleviate this issue, practitioners can rely on computing estimates of these distances over subsets of data, {\em i.e.} minibatches. While computationally appealing, we highlight in this paper some limits of this strategy, arguing it can lead to undesirable smoothing effects. As an alternative, we suggest that the same minibatch strategy coupled with unbalanced optimal transport can yield more robust behavior. We discuss the associated theoretical properties, such as unbiased estimators, existence of gradients and concentration bounds. Our experimental study shows that in challenging problems associated to domain adaptation, the use of unbalanced optimal transport leads to significantly better results, competing with or surpassing recent baselines.
Pictures of everyday life are inherently multi-label in nature. Hence, multi-label classification is commonly used to analyze their content. In typical multi-label datasets, each picture contains only a few positive labels, and many negative ones. This positive-negative imbalance can result in under-emphasizing gradients from positive labels during training, leading to poor accuracy. In this paper, we introduce a novel asymmetric loss ("ASL"), that operates differently on positive and negative samples. The loss dynamically down-weights the importance of easy negative samples, causing the optimization process to focus more on the positive samples, and also enables to discard mislabeled negative samples. We demonstrate how ASL leads to a more "balanced" network, with increased average probabilities for positive samples, and show how this balanced network is translated to better mAP scores, compared to commonly used losses. Furthermore, we offer a method that can dynamically adjust the level of asymmetry throughout the training. With ASL, we reach new state-of-the-art results on three common multi-label datasets, including achieving 86.6% on MS-COCO. We also demonstrate ASL applicability for other tasks such as fine-grain single-label classification and object detection. ASL is effective, easy to implement, and does not increase the training time or complexity. Implementation is available at: //github.com/Alibaba-MIIL/ASL.
Average precision (AP), the area under the recall-precision (RP) curve, is the standard performance measure for object detection. Despite its wide acceptance, it has a number of shortcomings, the most important of which are (i) the inability to distinguish very different RP curves, and (ii) the lack of directly measuring bounding box localization accuracy. In this paper, we propose 'Localization Recall Precision (LRP) Error', a new metric which we specifically designed for object detection. LRP Error is composed of three components related to localization, false negative (FN) rate and false positive (FP) rate. Based on LRP, we introduce the 'Optimal LRP', the minimum achievable LRP error representing the best achievable configuration of the detector in terms of recall-precision and the tightness of the boxes. In contrast to AP, which considers precisions over the entire recall domain, Optimal LRP determines the 'best' confidence score threshold for a class, which balances the trade-off between localization and recall-precision. In our experiments, we show that, for state-of-the-art object (SOTA) detectors, Optimal LRP provides richer and more discriminative information than AP. We also demonstrate that the best confidence score thresholds vary significantly among classes and detectors. Moreover, we present LRP results of a simple online video object detector which uses a SOTA still image object detector and show that the class-specific optimized thresholds increase the accuracy against the common approach of using a general threshold for all classes. We provide the source code that can compute LRP for the PASCAL VOC and MSCOCO datasets in //github.com/cancam/LRP. Our source code can easily be adapted to other datasets as well.
In this work we present a novel unsupervised framework for hard training example mining. The only input to the method is a collection of images relevant to the target application and a meaningful initial representation, provided e.g. by pre-trained CNN. Positive examples are distant points on a single manifold, while negative examples are nearby points on different manifolds. Both types of examples are revealed by disagreements between Euclidean and manifold similarities. The discovered examples can be used in training with any discriminative loss. The method is applied to unsupervised fine-tuning of pre-trained networks for fine-grained classification and particular object retrieval. Our models are on par or are outperforming prior models that are fully or partially supervised.
Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested processes and study the dependence structures they induce. Dependence ranges between homogeneity, corresponding to full exchangeability, and maximum heterogeneity, corresponding to (unconditional) independence across samples. The popular nested Dirichlet process is shown to degenerate to the fully exchangeable case when there are ties across samples at the observed or latent level. To overcome this drawback, inherent to nesting general discrete random measures, we introduce a novel class of latent nested processes. These are obtained by adding common and group-specific completely random measures and, then, normalising to yield dependent random probability measures. We provide results on the partition distributions induced by latent nested processes, and develop an Markov Chain Monte Carlo sampler for Bayesian inferences. A test for distributional homogeneity across groups is obtained as a by product. The results and their inferential implications are showcased on synthetic and real data.
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