These methods can approximate the likelihood through neural likelihood estimation (NLE) (Papamakarios et al., 2019) or directly target the posterior distribution with neural posterior estimation (NPE) (Greenberg et al., 2019; Lueckmann et al., 2017; Papamakarios and Murray, 2016), with NLE requiring subsequent Markov Chain Monte Carlo (MCMC) steps to produce posterior samples. The hallmark of these neural methods is their ability to accurately approximate complex posterior distributions using only forward simulations from the assumed model. While sequential methods iteratively refine the posterior estimate through multiple rounds of simulation, one-shot NPE and NLE methods perform inference in a single round, enabling amortized inference where a trained model can be reused for multiple datasets without retraining (see, e.g., Radev et al., 2020; Gloeckler et al., 2024). In particular, like the statistical methods of approximate Bayesian computation (ABC), see, e.g., Sisson et al. (2018) for a handbook treatment, and Martin et al. (2023) for a recent summary, and Bayesian synthetic likelihood (BSL), see, e.g., Wood (2010), Price et al. (2018) and Frazier et al. (2023), NPE and NLE first reduce the data down to a vector of statistics and then build an approximation to the resulting partial posterior by substituting likelihood evaluation with forward simulation from the assumed model. In contrast to the statistical methods for likelihood-free inference like ABC and BSL, NPE (respectively, NLE) approximates the posterior (resp., the likelihood) directly by fitting flexible conditional density estimators, usually neural-or flow-based approaches, using training data that is simulated from the assumed model space. The approximation that results from this training step is then directly used as a posterior in the context of NPE or as a likelihood in the case of NLE, with MCMC for this trained likelihood then used to produce draws from an approximate posterior.

The Pairwise Markov Chain (PMC) is a probabilistic graphical model extending the well-known Hidden Markov Model. This model, although highly effective for many tasks, has been scarcely utilized for continuous value prediction. This is mainly due to the issue of modeling observations inherent in generative probabilistic models. In this paper, we introduce a new algorithm for prediction with the PMC. On the one hand, this algorithm allows circumventing the feature problem, thus fully exploiting the capabilities of the PMC. On the other hand, it enables the PMC to extend any predictive model by introducing hidden states, updated at each time step, and allowing the introduction of non-stationarity for any model. We apply the PMC with its new algorithm for volatility forecasting, which we compare to the highly popular GARCH(1,1) and feedforward neural models across numerous pairs. This is particularly relevant given the regime changes that we can observe in volatility. For each scenario, our algorithm enhances the performance of the extended model, demonstrating the value of our approach.

Learning high-dimensional distributions is a significant challenge in machine learning and statistics. Classical research has mostly concentrated on asymptotic analysis of such data under suitable assumptions. While existing works [Bhattacharyya et al.: SICOMP 2023, Daskalakis et al.: STOC 2021, Choo et al.: ALT 2024] focus on discrete distributions, the current work addresses the tree structure learning problem for Gaussian distributions, providing efficient algorithms with solid theoretical guarantees. This is crucial as real-world distributions are often continuous and differ from the discrete scenarios studied in prior works. In this work, we design a conditional mutual information tester for Gaussian random variables that can test whether two Gaussian random variables are independent, or their conditional mutual information is at least $\varepsilon$, for some parameter $\varepsilon \in (0,1)$ using $\mathcal{O}(\varepsilon^{-1})$ samples which we show to be near-optimal. In contrast, an additive estimation would require $\Omega(\varepsilon^{-2})$ samples. Our upper bound technique uses linear regression on a pair of suitably transformed random variables. Importantly, we show that the chain rule of conditional mutual information continues to hold for the estimated (conditional) mutual information. As an application of such a mutual information tester, we give an efficient $\varepsilon$-approximate structure-learning algorithm for an $n$-variate Gaussian tree model that takes $\widetilde{\Theta}(n\varepsilon^{-1})$ samples which we again show to be near-optimal. In contrast, when the underlying Gaussian model is not known to be tree-structured, we show that $\widetilde{{{\Theta}}}(n^2\varepsilon^{-2})$ samples are necessary and sufficient to output an $\varepsilon$-approximate tree structure. We perform extensive experiments that corroborate our theoretical convergence bounds.

Model-based reinforcement learning refers to a set of approaches capable of sample-efficient decision making, which create an explicit model of the environment. This model can subsequently be used for learning optimal policies. In this paper, we propose a temporal Gaussian Mixture Model composed of a perception model and a transition model. The perception model extracts discrete (latent) states from continuous observations using a variational Gaussian mixture likelihood. Importantly, our model constantly monitors the collected data searching for new Gaussian components, i.e., the perception model performs a form of structure learning (Smith et al., 2020; Friston et al., 2018; Neacsu et al., 2022) as it learns the number of Gaussian components in the mixture. Additionally, the transition model learns the temporal transition between consecutive time steps by taking advantage of the Dirichlet-categorical conjugacy. Both the perception and transition models are able to forget part of the data points, while integrating the information they provide within the prior, which ensure fast variational inference. Finally, decision making is performed with a variant of Q-learning which is able to learn Q-values from beliefs over states. Empirically, we have demonstrated the model's ability to learn the structure of several mazes: the model discovered the number of states and the transition probabilities between these states. Moreover, using its learned Q-values, the agent was able to successfully navigate from the starting position to the maze's exit.

We propose a unifying framework for methods that perform Bayesian online learning in non-stationary environments. We call the framework BONE, which stands for (B)ayesian (O)nline learning in (N)on-stationary (E)nvironments. BONE provides a common structure to tackle a variety of problems, including online continual learning, prequential forecasting, and contextual bandits. The framework requires specifying three modelling choices: (i) a model for measurements (e.g., a neural network), (ii) an auxiliary process to model non-stationarity (e.g., the time since the last changepoint), and (iii) a conditional prior over model parameters (e.g., a multivariate Gaussian). The framework also requires two algorithmic choices, which we use to carry out approximate inference under this framework: (i) an algorithm to estimate beliefs (posterior distribution) about the model parameters given the auxiliary variable, and (ii) an algorithm to estimate beliefs about the auxiliary variable. We show how this modularity allows us to write many different existing methods as instances of BONE; we also use this framework to propose a new method. We then experimentally compare existing methods with our proposed new method on several datasets; we provide insights into the situations that make one method more suitable than another for a given task.

We consider the fundamental problem of learning the parameters of an undirected graphical model or Markov Random Field (MRF) in the setting where the edge weights are chosen at random. For Ising models, we show that a multiplicative-weight update algorithm due to Klivans and Meka learns the parameters in polynomial time for any inverse temperature $\beta \leq \sqrt{\log n}$. This immediately yields an algorithm for learning the Sherrington-Kirkpatrick (SK) model beyond the high-temperature regime of $\beta < 1$. Prior work breaks down at $\beta = 1$ and requires heavy machinery from statistical physics or functional inequalities. In contrast, our analysis is relatively simple and uses only subgaussian concentration. Our results extend to MRFs of higher order (such as pure $p$-spin models), where even results in the high-temperature regime were not known.

This study presents a comparative analysis of two objective functions, Mean Squared Error (MSE) and Softmax Cross-Entropy (SCE) for neural network classification tasks. While SCE combined with softmax activation is the conventional choice for transforming network outputs into class probabilities, we explore an alternative approach using MSE with sigmoid activation. We introduce the Output Reset algorithm, which reduces inconsistent errors and enhances classifier robustness. Through extensive experiments on benchmark datasets (MNIST, CIFAR-10, and Fashion-MNIST), we demonstrate that MSE with sigmoid activation achieves comparable accuracy and convergence rates to SCE, while exhibiting superior performance in scenarios with noisy data. Our findings indicate that MSE, despite its traditional association with regression tasks, serves as a viable alternative for classification problems, challenging conventional wisdom about neural network training strategies.

Imagine searching a collection of coins for quarters ($0.25$), dimes ($0.10$), nickels ($0.05$), and pennies ($0.01$)-a hybrid foraging task where observers look for multiple instances of multiple target types. In such tasks, how do target values and their prevalence influence foraging and eye movement behaviors (e.g., should you prioritize rare quarters or common nickels)? To explore this, we conducted human psychophysics experiments, revealing that humans are proficient reward foragers. Their eye fixations are drawn to regions with higher average rewards, fixation durations are longer on more valuable targets, and their cumulative rewards exceed chance, approaching the upper bound of optimal foragers. To probe these decision-making processes of humans, we developed a transformer-based Visual Forager (VF) model trained via reinforcement learning. Our VF model takes a series of targets, their corresponding values, and the search image as inputs, processes the images using foveated vision, and produces a sequence of eye movements along with decisions on whether to collect each fixated item. Our model outperforms all baselines, achieves cumulative rewards comparable to those of humans, and approximates human foraging behavior in eye movements and foraging biases within time-limited environments. Furthermore, stress tests on out-of-distribution tasks with novel targets, unseen values, and varying set sizes demonstrate the VF model's effective generalization. Our work offers valuable insights into the relationship between eye movements and decision-making, with our model serving as a powerful tool for further exploration of this connection. All data, code, and models will be made publicly available.

Reinforcement learning algorithms are usually stated without theoretical guarantees regarding their performance. Recently, Jin, Yang, Wang, and Jordan (COLT 2020) showed a polynomial-time reinforcement learning algorithm (namely, LSVI-UCB) for the setting of linear Markov decision processes, and provided theoretical guarantees regarding its running time and regret. In real-world scenarios, however, the space usage of this algorithm can be prohibitive due to a utilized linear regression step. We propose and analyze two modifications of LSVI-UCB, which alternate periods of learning and not-learning, to reduce space and time usage while maintaining sublinear regret. We show experimentally, on synthetic data and real-world benchmarks, that our algorithms achieve low space usage and running time, while not significantly sacrificing regret.

Recent progress in interactive point prompt based Image Segmentation allows to significantly reduce the manual effort to obtain high quality semantic labels. State-of-the-art unsupervised methods use self-supervised pre-trained models to obtain pseudo-labels which are used in training a prompt-based segmentation model. In this paper, we propose a novel unsupervised and training-free approach based solely on the self-attention of Stable Diffusion. We interpret the self-attention tensor as a Markov transition operator, which enables us to iteratively construct a Markov chain. Pixel-wise counting of the required number of iterations along the Markov-chain to reach a relative probability threshold yields a Markov-iteration-map, which we simply call a Markov-map. Compared to the raw attention maps, we show that our proposed Markov-map has less noise, sharper semantic boundaries and more uniform values within semantically similar regions. We integrate the Markov-map in a simple yet effective truncated nearest neighbor framework to obtain interactive point prompt based segmentation. Despite being training-free, we experimentally show that our approach yields excellent results in terms of Number of Clicks (NoC), even outperforming state-of-the-art training based unsupervised methods in most of the datasets.