Neural Information Processing Systems http://nips.cc/

We prove uniqueness of the barycenter of a population of GPs, as well as convergence of the metric and the barycenter of their finite-dimensional counterparts.

One such estimation is maximum mean discrepancy (MMD).

We develop a convex safe approximation of the minimax formulation and show that such approximation renders a nearly-optimal detector among the family of all possible tests.

We describe how BWGAN can be efficiently implemented.

The geometry of dynamical systems estimated from trajectory data is a major challenge for machine learning applications. Koopman and transfer operators provide a linear representation of nonlinear dynamics through their spectral decomposition, offering a natural framework for comparison. We propose a novel approach representing each system as a distribution of its joint operator eigenvalues and spectral projectors and defining a metric between systems leveraging optimal transport. The proposed metric is invariant to the sampling frequency of trajectories. It is also computationally efficient, supported by finite-sample convergence guarantees, and enables the computation of Fr echet means, providing interpolation between dynamical systems. Experiments on simulated and real-world datasets show that our approach consistently outperforms standard operator-based distances in machine learning applications, including dimensionality reduction and classification, and provides meaningful interpolation between dynamical systems. Dynamical systems are widely used across scientific and engineering disciplines to model state variables' evolution over time (Lasota & Mackey, 2013). Nonlinear ordinary or partial differential equations typically govern these systems and may incorporate stochastic components (Meyn & Tweedie, 2012). However, in many practical situations, analytical models are unavailable or intractable, motivating the use of data-driven approaches to infer the underlying dynamics from sampled trajectories. In this context, Koopman and transfer operator regressions have emerged as a powerful framework for learning and interpreting dynamical systems from data (Brunton et al., 2022). Rather than directly modeling the evolution of state variables, these operators advance observables (scalar functions defined on the state space) by mapping each to its expected future value conditioned on the current state. Crucially, these operators are linear even when the underlying systems are not linear.

Recently, many bias detection methods have been proposed to determine the level of bias a large language model captures. However, tests to identify which parts of a large language model are responsible for bias towards specific groups remain underdeveloped. In this study, we present a method using topological data analysis to identify which heads in GPT-2 contribute to the misrepresentation of identity groups present in the StereoSet dataset. We find that biases for particular categories, such as gender or profession, are concentrated in attention heads that act as hot spots. The metric we propose can also be used to determine which heads capture bias for a specific group within a bias category, and future work could extend this method to help de-bias large language models.

In this paper, we tackle the dynamic mean-variance portfolio selection problem in a {\it model-free} manner, based on (generative) diffusion models. We propose using data sampled from the real model $\mathbb P$ (which is unknown) with limited size to train a generative model $\mathbb Q$ (from which we can easily and adequately sample). With adaptive training and sampling methods that are tailor-made for time series data, we obtain quantification bounds between $\mathbb P$ and $\mathbb Q$ in terms of the adapted Wasserstein metric $\mathcal A W_2$. Importantly, the proposed adapted sampling method also facilitates {\it conditional sampling}. In the second part of this paper, we provide the stability of the mean-variance portfolio optimization problems in $\mathcal A W _2$. Then, combined with the error bounds and the stability result, we propose a policy gradient algorithm based on the generative environment, in which our innovative adapted sampling method provides approximate scenario generators. We illustrate the performance of our algorithm on both simulated and real data. For real data, the algorithm based on the generative environment produces portfolios that beat several important baselines, including the Markowitz portfolio, the equal weight (naive) portfolio, and S\&P 500.

The Wasserstein metric has become increasingly important in many machine learning applications such as generative modeling, image retrieval and domain adaptation. Despite its appeal, it is often too costly to compute. This has motivated approximation methods like entropy-regularized optimal transport, downsampling, and subsampling, which trade accuracy for computational efficiency. In this paper, we consider the challenge of computing efficient approximations to the Wasserstein metric that also serve as strict upper or lower bounds. Focusing on discrete measures on regular grids, our approach involves formulating and exactly solving a Kantorovich problem on a coarse grid using a quantized measure and specially designed cost matrix, followed by an upscaling and correction stage. This is done either in the primal or dual space to obtain valid upper and lower bounds on the Wasserstein metric of the full-resolution inputs. We evaluate our methods on the DOTmark optimal transport images benchmark, demonstrating a 10x-100x speedup compared to entropy-regularized OT while keeping the approximation error below 2%.

Hybrid action models are widely considered an effective approach to reinforcement learning (RL) modeling. The current mainstream method is to train agents under Parameterized Action Markov Decision Processes (PAMDPs), which performs well in specific environments. Unfortunately, these models either exhibit drastic low learning efficiency in complex PAMDPs or lose crucial information in the conversion between raw space and latent space. To enhance the learning efficiency and asymptotic performance of the agent, we propose a model-based RL (MBRL) algorithm, FLEXplore. FLEXplore learns a parameterized-action-conditioned dynamics model and employs a modified Model Predictive Path Integral control. Unlike conventional MBRL algorithms, we carefully design the dynamics loss function and reward smoothing process to learn a loose yet flexible model. Additionally, we use the variational lower bound to maximize the mutual information between the state and the hybrid action, enhancing the exploration effectiveness of the agent. We theoretically demonstrate that FLEXplore can reduce the regret of the rollout trajectory through the Wasserstein Metric under given Lipschitz conditions. Our empirical results on several standard benchmarks show that FLEXplore has outstanding learning efficiency and asymptotic performance compared to other baselines.