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Generative models have proven to be an outstanding tool for representing high-dimensional probability distributions and generating realistic-looking images. An essential characteristic of generative models is their ability to produce multi-modal outputs. However, while training, they are often susceptible to mode collapse, that is models are limited in mapping input noise to only a few modes of the true data distribution. In this work, we draw inspiration from Determinantal Point Process (DPP) to propose an unsupervised penalty loss that alleviates mode collapse while producing higher quality samples. DPP is an elegant probabilistic measure used to model negative correlations within a subset and hence quantify its diversity. We use DPP kernel to model the diversity in real data as well as in synthetic data. Then, we devise an objective term that encourages generators to synthesize data with similar diversity to real data. In contrast to previous state-of-the-art generative models that tend to use additional trainable parameters or complex training paradigms, our method does not change the original training scheme. Embedded in an adversarial training and variational autoencoder, our Generative DPP approach shows a consistent resistance to mode-collapse on a wide variety of synthetic data and natural image datasets including MNIST, CIFAR10, and CelebA, while outperforming state-of-the-art methods for data-efficiency, generation quality, and convergence-time whereas being 5.8x faster than its closest competitor.
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Although significant progress has been made in the field of automatic image captioning, it is still a challenging task. Previous works normally pay much attention to improving the quality of the generated captions but ignore the diversity of captions. In this paper, we combine determinantal point process (DPP) and reinforcement learning (RL) and propose a novel reinforcing DPP (R-DPP) approach to generate a set of captions with high quality and diversity for an image. We show that R-DPP performs better on accuracy and diversity than using noise as a control signal (GANs, VAEs). Moreover, R-DPP is able to preserve the modes of the learned distribution. Hence, beam search algorithm can be applied to generate a single accurate caption, which performs better than other RL-based models.
Semi-parametric regression models are used in several applications which require comprehensibility without sacrificing accuracy. Typical examples are spline interpolation in geophysics, or non-linear time series problems, where the system includes a linear and non-linear component. We discuss here the use of a finite Determinantal Point Process (DPP) for approximating semi-parametric models. Recently, Barthelme, Tremblay, Usevich, and Amblard introduced a novel representation of some finite DPPs. These authors formulated extended L-ensembles that can conveniently represent partial-projection DPPs and suggest their use for optimal interpolation. With the help of this formalism, we derive a key identity illustrating the implicit regularization effect of determinantal sampling for semi-parametric regression and interpolation. Also, a novel projected Nystrom approximation is defined and used to derive a bound on the expected risk for the corresponding approximation of semi-parametric regression. This work naturally extends similar results obtained for kernel ridge regression.
Event sequences can be modeled by temporal point processes (TPPs) to capture their asynchronous and probabilistic nature. We propose an intensity-free framework that directly models the point process distribution by utilizing normalizing flows. This approach is capable of capturing highly complex temporal distributions and does not rely on restrictive parametric forms. Comparisons with state-of-the-art baseline models on both synthetic and challenging real-life datasets show that the proposed framework is effective at modeling the stochasticity of discrete event sequences.
Determinantal point processes (DPPs) are popular probabilistic models of diversity. In this paper, we investigate DPPs from a new perspective: property testing of distributions. Given sample access to an unknown distribution $q$ over the subsets of a ground set, we aim to distinguish whether $q$ is a DPP distribution, or $epsilon$-far from all DPP distributions in $ell_1$-distance. In this work, we propose the first algorithm for testing DPPs. Furthermore, we establish a matching lower bound on the sample complexity of DPP testing. This lower bound also extends to showing a new hardness result for the problem of testing the more general class of log-submodular distributions.
In this paper, we investigate the impact of diverse user preference on learning under the stochastic multi-armed bandit (MAB) framework. We aim to show that when the user preferences are sufficiently diverse and each arm can be optimal for certain users, the O(log T) regret incurred by exploring the sub-optimal arms under the standard stochastic MAB setting can be reduced to a constant. Our intuition is that to achieve sub-linear regret, the number of times an optimal arm being pulled should scale linearly in time; when all arms are optimal for certain users and pulled frequently, the estimated arm statistics can quickly converge to their true values, thus reducing the need of exploration dramatically. We cast the problem into a stochastic linear bandits model, where both the users preferences and the state of arms are modeled as {independent and identical distributed (i.i.d)} d-dimensional random vectors. After receiving the user preference vector at the beginning of each time slot, the learner pulls an arm and receives a reward as the linear product of the preference vector and the arm state vector. We also assume that the state of the pulled arm is revealed to the learner once its pulled. We propose a Weighted Upper Confidence Bound (W-UCB) algorithm and show that it can achieve a constant regret when the user preferences are sufficiently diverse. The performance of W-UCB under general setups is also completely characterized and validated with synthetic data.
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