Demystifying Softmax Gating in Gaussian Mixture of Experts

Understanding parameter estimation of softmax gating Gaussian mixture of experts has remained a long-standing open problem in the literature. It is mainly due to three fundamental theoretical challenges associated with the softmax gating: (i) the identifiability only up to the translation of the parameters; (ii) the intrinsic interaction via partial differential equation between the softmax gating and the expert functions in Gaussian distribution; (iii) the complex dependence between the numerator and denominator of the conditional density of softmax gating Gaussian mixture of experts. We resolve these challenges by proposing novel Vononoi loss functions among parameters and establishing the convergence rates of the maximum likelihood estimator (MLE) for solving parameter estimation in these models. When the number of experts is unknown and over-specified, our findings show a connection between the rate of MLE and a solvability problem of a system of polynomial equations.

Aerial-Ground Person Re-ID

Person re-ID matches persons across multiple non-overlapping cameras. Despite the increasing deployment of airborne platforms in surveillance, current existing person re-ID benchmarks' focus is on ground-ground matching and very limited efforts on aerial-aerial matching. We propose a new benchmark dataset - AG-ReID, which performs person re-ID matching in a new setting: across aerial and ground cameras. Our dataset contains 21,983 images of 388 identities and 15 soft attributes for each identity. The data was collected by a UAV flying at altitudes between 15 to 45 meters and a ground-based CCTV camera on a university campus. Our dataset presents a novel elevated-viewpoint challenge for person re-ID due to the significant difference in person appearance across these cameras. We propose an explainable algorithm to guide the person re-ID model's training with soft attributes to address this challenge. Experiments demonstrate the efficacy of our method on the aerial-ground person re-ID task. The dataset will be published and the baseline codes will be open-sourced at https://github.com/huynguyen792/AG-ReID to facilitate research in this area.

AutoWS: Automated Weak Supervision Framework for Text Classification

Creating large, good quality labeled data has become one of the major bottlenecks for developing machine learning applications. Multiple techniques have been developed to either decrease the dependence of labeled data (zero/few-shot learning, weak supervision) or to improve the efficiency of labeling process (active learning). Among those, Weak Supervision has been shown to reduce labeling costs by employing hand crafted labeling functions designed by domain experts. We propose AutoWS -- a novel framework for increasing the efficiency of weak supervision process while decreasing the dependency on domain experts. Our method requires a small set of labeled examples per label class and automatically creates a set of labeling functions to assign noisy labels to numerous unlabeled data. Noisy labels can then be aggregated into probabilistic labels used by a downstream discriminative classifier. Our framework is fully automatic and requires no hyper-parameter specification by users. We compare our approach with different state-of-the-art work on weak supervision and noisy training. Experimental results show that our method outperforms competitive baselines.

Fast Approximation of the Generalized Sliced-Wasserstein Distance

Generalized sliced Wasserstein distance is a variant of sliced Wasserstein distance that exploits the power of non-linear projection through a given defining function to better capture the complex structures of the probability distributions. Similar to sliced Wasserstein distance, generalized sliced Wasserstein is defined as an expectation over random projections which can be approximated by the Monte Carlo method. However, the complexity of that approximation can be expensive in high-dimensional settings. To that end, we propose to form deterministic and fast approximations of the generalized sliced Wasserstein distance by using the concentration of random projections when the defining functions are polynomial function, circular function, and neural network type function. Our approximations hinge upon an important result that one-dimensional projections of a high-dimensional random vector are approximately Gaussian.

Hierarchical Sliced Wasserstein Distance

Sliced Wasserstein (SW) distance has been widely used in different application scenarios since it can be scaled to a large number of supports without suffering from the curse of dimensionality. The value of sliced Wasserstein distance is the average of transportation cost between one-dimensional representations (projections) of original measures that are obtained by Radon Transform (RT). Despite its efficiency in the number of supports, estimating the sliced Wasserstein requires a relatively large number of projections in high-dimensional settings. Therefore, for applications where the number of supports is relatively small compared with the dimension, e.g., several deep learning applications where the mini-batch approaches are utilized, the complexities from matrix multiplication of Radon Transform become the main computational bottleneck. To address this issue, we propose to derive projections by linearly and randomly combining a smaller number of projections which are named bottleneck projections. We explain the usage of these projections by introducing Hierarchical Radon Transform (HRT) which is constructed by applying Radon Transform variants recursively. We then formulate the approach into a new metric between measures, named Hierarchical Sliced Wasserstein (HSW) distance. By proving the injectivity of HRT, we derive the metricity of HSW. Moreover, we investigate the theoretical properties of HSW including its connection to SW variants and its computational and sample complexities. Finally, we compare the computational cost and generative quality of HSW with the conventional SW on the task of deep generative modeling using various benchmark datasets including CIFAR10, CelebA, and Tiny ImageNet.

Predicting Performances of Mutual Funds using Deep Learning and Ensemble Techniques

Predicting fund performance is beneficial to both investors and fund managers, and yet is a challenging task. In this paper, we have tested whether deep learning models can predict fund performance more accurately than traditional statistical techniques. Fund performance is typically evaluated by the Sharpe ratio, which represents the risk-adjusted performance to ensure meaningful comparability across funds. We calculated the annualised Sharpe ratios based on the monthly returns time series data for more than 600 open-end mutual funds investing in listed large-cap equities in the United States. We find that long short-term memory (LSTM) and gated recurrent units (GRUs) deep learning methods, both trained with modern Bayesian optimization, provide higher accuracy in forecasting funds' Sharpe ratios than traditional statistical ones. An ensemble method, which combines forecasts from LSTM and GRUs, achieves the best performance of all models. There is evidence to say that deep learning and ensembling offer promising solutions in addressing the challenge of fund performance forecasting.

Robust Product Classification with Instance-Dependent Noise

Noisy labels in large E-commerce product data (i.e., product items are placed into incorrect categories) are a critical issue for product categorization task because they are unavoidable, non-trivial to remove and degrade prediction performance significantly. Training a product title classification model which is robust to noisy labels in the data is very important to make product classification applications more practical. In this paper, we study the impact of instance-dependent noise to performance of product title classification by comparing our data denoising algorithm and different noise-resistance training algorithms which were designed to prevent a classifier model from over-fitting to noise. We develop a simple yet effective Deep Neural Network for product title classification to use as a base classifier. Along with recent methods of stimulating instance-dependent noise, we propose a novel noise stimulation algorithm based on product title similarity. Our experiments cover multiple datasets, various noise methods and different training solutions. Results uncover the limit of classification task when noise rate is not negligible and data distribution is highly skewed.