Particle-based deep generative models, such as gradient flows and score-based diffusion models, have recently gained traction thanks to their striking performance. Their principle of displacing particle distributions using differential equations is conventionally seen as opposed to the previously widespread generative adversarial networks (GANs), which involve training a pushforward generator network. In this paper we challenge this interpretation, and propose a novel framework that unifies particle and adversarial generative models by framing generator training as a generalization of particle models. This suggests that a generator is an optional addition to any such generative model. Consequently, integrating a generator into a score-based diffusion model and training a GAN without a generator naturally emerge from our framework. We empirically test the viability of these original models as proofs of concepts of potential applications of our framework.

Safeguarding privacy in sensitive training data is paramount, particularly in the context of generative modeling. This is done through either differentially private stochastic gradient descent, or with a differentially private metric for training models or generators. In this paper, we introduce a novel differentially private generative modeling approach based on parameter-free gradient flows in the space of probability measures. The proposed algorithm is a new discretized flow which operates through a particle scheme, utilizing drift derived from the sliced Wasserstein distance and computed in a private manner. Our experiments show that compared to a generator-based model, our proposed model can generate higher-fidelity data at a low privacy budget, offering a viable alternative to generator-based approaches.

Data-to-text (D2T) and text-to-data (T2D) are dual tasks that convert structured data, such as graphs or tables into fluent text, and vice versa. These tasks are usually handled separately and use corpora extracted from a single source. Current systems leverage pre-trained language models fine-tuned on D2T or T2D tasks. This approach has two main limitations: first, a separate system has to be tuned for each task and source; second, learning is limited by the scarcity of available corpora. This paper considers a more general scenario where data are available from multiple heterogeneous sources. Each source, with its specific data format and semantic domain, provides a non-parallel corpus of text and structured data. We introduce a variational auto-encoder model with disentangled style and content variables that allows us to represent the diversity that stems from multiple sources of text and data. Our model is designed to handle the tasks of D2T and T2D jointly. We evaluate our model on several datasets, and show that by learning from multiple sources, our model closes the performance gap with its supervised single-source counterpart and outperforms it in some cases.

A determinantal point process (DPP) is an elegant model that assigns a probability to every subset of a collection of $n$ items. While conventionally a DPP is parameterized by a symmetric kernel matrix, removing this symmetry constraint, resulting in nonsymmetric DPPs (NDPPs), leads to significant improvements in modeling power and predictive performance. Recent work has studied an approximate Markov chain Monte Carlo (MCMC) sampling algorithm for NDPPs restricted to size-$k$ subsets (called $k$-NDPPs). However, the runtime of this approach is quadratic in $n$, making it infeasible for large-scale settings. In this work, we develop a scalable MCMC sampling algorithm for $k$-NDPPs with low-rank kernels, thus enabling runtime that is sublinear in $n$. Our method is based on a state-of-the-art NDPP rejection sampling algorithm, which we enhance with a novel approach for efficiently constructing the proposal distribution. Furthermore, we extend our scalable $k$-NDPP sampling algorithm to NDPPs without size constraints. Our resulting sampling method has polynomial time complexity in the rank of the kernel, while the existing approach has runtime that is exponential in the rank. With both a theoretical analysis and experiments on real-world datasets, we verify that our scalable approximate sampling algorithms are orders of magnitude faster than existing sampling approaches for $k$-NDPPs and NDPPs.

A determinantal point process (DPP) on a collection of $M$ items is a model, parameterized by a symmetric kernel matrix, that assigns a probability to every subset of those items. Recent work shows that removing the kernel symmetry constraint, yielding nonsymmetric DPPs (NDPPs), can lead to significant predictive performance gains for machine learning applications. However, existing work leaves open the question of scalable NDPP sampling. There is only one known DPP sampling algorithm, based on Cholesky decomposition, that can directly apply to NDPPs as well. Unfortunately, its runtime is cubic in $M$, and thus does not scale to large item collections. In this work, we first note that this algorithm can be transformed into a linear-time one for kernels with low-rank structure. Furthermore, we develop a scalable sublinear-time rejection sampling algorithm by constructing a novel proposal distribution. Additionally, we show that imposing certain structural constraints on the NDPP kernel enables us to bound the rejection rate in a way that depends only on the kernel rank. In our experiments we compare the speed of all of these samplers for a variety of real-world tasks.

Determinantal point processes (DPPs) have attracted significant attention from the machine learning community for their ability to model subsets drawn from a large collection of items. Recent work shows that nonsymmetric DPP kernels have significant advantages over symmetric kernels in terms of modeling power and predictive performance. However, the nonsymmetric kernel learning algorithm from prior work has computational complexity that is cubic in the size of the DPP ground set, from which subsets are drawn, making it impractical to use at large scales. In this work, we propose a new decomposition for nonsymmetric DPP kernels that induces linear-time complexity for learning and approximate maximum a posteriori (MAP) inference. We also prove a lower bound on the quality of this MAP approximation. Through evaluation on real-world datasets, we show that our new decomposition not only scales better, but also matches or exceeds the predictive performance of prior work.

Embedding models, which learn latent representations of users and items based on user-item interaction patterns, are a key component of recommendation systems. In many applications, contextual constraints need to be applied to refine recommendations, e.g. when a user specifies a price range or product category filter. The conventional approach, for both context-aware and standard models, is to retrieve items and apply the constraints as independent operations. The order in which these two steps are executed can induce significant problems. For example, applying constraints a posteriori can result in incomplete recommendations or low-quality results for the tail of the distribution (i.e., less popular items). As a result, the additional information that the constraint brings about user intent may not be accurately captured. In this paper we propose integrating the information provided by the contextual constraint into the similarity computation, by merging constraint application and retrieval into one operation in the embedding space. This technique allows us to generate high-quality recommendations for the specified constraint. Our approach learns constraints representations jointly with the user and item embeddings. We incorporate our methods into a matrix factorization model, and perform an experimental evaluation on one internal and two real-world datasets. Our results show significant improvements in predictive performance compared to context-aware and standard models.

Determinantal point processes (DPPs) have attracted substantial attention as an elegant probabilistic model that captures the balance between quality and diversity within sets. DPPs are conventionally parameterized by a positive semi-definite kernel matrix, and this symmetric kernel encodes only repulsive interactions between items. These so-called symmetric DPPs have significant expressive power, and have been successfully applied to a variety of machine learning tasks, including recommendation systems, information retrieval, and automatic summarization, among many others. Efficient algorithms for learning symmetric DPPs and sampling from these models have been reasonably well studied. However, relatively little attention has been given to nonsymmetric DPPs, which relax the symmetric constraint on the kernel. Nonsymmetric DPPs allow for both repulsive and attractive item interactions, which can significantly improve modeling power, resulting in a model that may better fit for some applications. We present a method that enables a tractable algorithm, based on maximum likelihood estimation, for learning nonsymmetric DPPs from data composed of observed subsets. Our method imposes a particular decomposition of the nonsymmetric kernel that enables such tractable learning algorithms, which we analyze both theoretically and experimentally. We evaluate our model on synthetic and real-world datasets, demonstrating improved predictive performance compared to symmetric DPPs, which have previously shown strong performance on modeling tasks associated with these datasets.

Determinantal point processes (DPPs) have attracted significant attention as an elegant model that is able to capture the balance between quality and diversity within sets. DPPs are parameterized by a positive semi-definite kernel matrix. While DPPs have substantial expressive power, they are fundamentally limited by the parameterization of the kernel matrix and their inability to capture nonlinear interactions between items within sets. We present the deep DPP model as way to address these limitations, by using a deep feed-forward neural network to learn the kernel matrix. In addition to allowing us to capture nonlinear item interactions, the deep DPP also allows easy incorporation of item metadata into DPP learning. We show experimentally that the deep DPP can provide a considerable improvement in the predictive performance of DPPs.

Determinantal point processes (DPPs) have received significant attention in the recent years as an elegant model for a variety of machine learning tasks, due to their ability to elegantly model set diversity and item quality or popularity. Recent work has shown that DPPs can be effective models for product recommendation and basket completion tasks. We present an enhanced DPP model that is specialized for the task of basket completion, the multi-task DPP. We view the basket completion problem as a multi-class classification problem, and leverage ideas from tensor factorization and multi-class classification to design the multi-task DPP model. We evaluate our model on several real-world datasets, and find that the multi-task DPP provides significantly better predictive quality than a number of state-of-the-art models.