AISTATS 2023 Papers

Many dynamical systems in the real world are naturally described by latent states with intrinsic ordering, such as “ally”, “neutral”, and “enemy” relationships in international relations. These latent states manifest through countries’ cooperative versus conflictual interactions over time. State-space models (SSMs) explicitly relate the dynamics of observed measurements to transitions in latent states. For discrete data, SSMs commonly do so through a state-to-action emission matrix and a state-to-state transition matrix. This paper introduces the Ordered Matrix Dirichlet (OMD) as a prior distribution over ordered stochastic matrices wherein the discrete distribution in the kth row is stochastically dominated by the (k+1)th, such that probability mass is shifted to the right when moving down rows. We illustrate the OMD prior within two SSMs: a hidden Markov model, and a novel dynamic Poisson Tucker decomposition model tailored to international relations data. We find that models built on the OMD recover interpretable ordered latent structure without forfeiting predictive performance. We suggest future applications to other domains where models with stochastic matrices are popular (e.g., topic modeling), and publish user-friendly code.

The Bayesian Learning Rule provides a framework for generic algorithm design but can be difficult to use for three reasons. First, it requires a specific parameterization of exponential family. Second, it uses gradients which can be difficult to compute. Third, its update may not always stay on the manifold. We address these difficulties by proposing an extension based on Lie-groups where posteriors are parametrized through transformations of an arbitrary base distribution and updated via the group’s exponential map. This simplifies all three difficulties for many cases, providing flexible parametrizations through group’s action, simple gradient computation through reparameterization, and updates that always stay on the manifold. We use the new learning rule to derive a new algorithm for deep learning with desirable biologically-plausible attributes to learn sparse features. Our work opens a new frontier for the design of new algorithms by exploiting lie-group structures.

Graphical models such as Markov random fields (MRFs) that are associated with undirected graphs, and Bayesian networks (BNs) that are associated with directed acyclic graphs, have proven to be a very popular approach for reasoning under uncertainty, prediction problems and causal inference. Parametric MRF likelihoods are well-studied for Gaussian and categorical data. However, in more complicated parametric and semi-parametric settings, likelihoods specified via clique potential functions are generally not known to be congenial or non-redundant. Congenial and non-redundant DAG likelihoods are far simpler to specify in both parametric and semi-parametric settings by modeling Markov factors in the DAG factorization. However, DAG likelihoods specified in this way are not guaranteed to coincide in distinct DAGs within the same Markov equivalence class. This complicates likelihoods based model selection procedures for DAGs by “sneaking in” potentially unwarranted assumptions about edge orientations. In this paper we link a density function decomposition due to Chen with the clique factorization of MRFs described by Lauritzen to provide a general likelihood for MRF models. The proposed likelihood is composed of variationally independent, and non-redundant closed form functionals of the observed data distribution, and is sufficiently general to apply to arbitrary parametric and semi-parametric models. We use an extension of our developments to give a general likelihood for DAG models that is guaranteed to coincide for all members of a Markov equivalence class. Our results have direct applications for model selection and semi-parametric inference.

The central objective function of a variational autoencoder (VAE) is its variational lower bound (the ELBO). Here we show that for standard (i.e., Gaussian) VAEs the ELBO converges to a value given by the sum of three entropies: the (negative) entropy of the prior distribution, the expected (negative) entropy of the observable distribution, and the average entropy of the variational distributions (the latter is already part of the ELBO). Our derived analytical results are exact and apply for small as well as for intricate deep networks for encoder and decoder. Furthermore, they apply for finitely and infinitely many data points and at any stationary point (including local maxima and saddle points). The result implies that the ELBO can for standard VAEs often be computed in closed-form at stationary points while the original ELBO requires numerical approximations of integrals. As a main contribution, we provide the proof that the ELBO for VAEs is at stationary points equal to entropy sums. Numerical experiments then show that the obtained analytical results are sufficiently precise also in those vicinities of stationary points that are reached in practice. Furthermore, we discuss how the novel entropy form of the ELBO can be used to analyze and understand learning behavior. More generally, we believe that our contributions can be useful for future theoretical and practical studies on VAE learning as they provide novel information on those points in parameters space that optimization of VAEs converges to.

Sampling over combinatorial spaces is a fundamental problem in artificial intelligence with a wide variety of applications. Since state-of-the-art techniques heavily rely on heuristics whose rigorous analysis remains beyond the reach of current theoretical tools, the past few years have witnessed interest in the design of techniques to test the quality of samplers. The current state-of-the-art techniques, $\mathsf{Barbarik}$ and $\mathsf{Barbarik2}$, focuses on the cases where combinatorial spaces are encoded as Conjunctive Normal Form (CNF) formulas. While CNF is a general-purpose form, often techniques rely on exploiting specific representations to achieve speedup. Of particular interest are Horn clauses, which form the basis of the logic programming tools in AI. In this context, a natural question is whether it is possible to design a tester that can determine the correctness of a given Horn sampler. The primary contribution of this paper is an affirmative answer to the above question. We design the first tester, $\mathsf{Flash}$, which tests the correctness of a given Horn sampler: given a specific distribution $\mathcal{I}$ and parameters $\eta$, $\varepsilon$, and $\delta$, the tester $\mathsf{Flash}$ correctly (with probability at least $ 1-\delta$) distinguishes whether the underlying distribution of the Horn-sampler is “$\varepsilon$-close” to $\mathcal{I}$ or “$\eta$-far” from $\mathcal{I}$ by sampling only $\widetilde{\mathcal{O}}(\mathsf{tilt}^3/(\eta - \varepsilon)^4)$ samples from the Horn-sampler, where the $\mathsf{tilt}$ is the ratio of the maximum and the minimum (non-zero) probability masses of $\mathcal{I}$. We also provide a prototype implementation of $\mathsf{Flash}$ and test three state-of-the-art samplers on a set of benchmarks.

Kernel machines are one of the most studied family of methods in machine learning. In the exact setting, training requires to instantiate the kernel matrix, thereby prohibiting their application to large-sampled data. One popular kernel approximation strategy which allows to tackle large-sampled data consists in interpolating product kernels on a set of grid-structured inducing points. However, since the number of model parameters increases exponentially with the dimensionality of the data, these methods are limited to small-dimensional datasets. In this work we lift this limitation entirely by placing inducing points on a grid and constraining the primal weights to be a low-rank Canonical Polyadic Decomposition. We derive a block coordinate descent algorithm that efficiently exploits grid-structured inducing points. The computational complexity of the algorithm scales linearly both in the number of samples and in the dimensionality of the data for any product kernel. We demonstrate the performance of our algorithm on large-scale and high-dimensional data, achieving state-of-the art results on a laptop computer. Our results show that grid-structured approaches can work in higher-dimensional problems.

This paper proposes a temporal graph neural network model for forecasting of graph-structured irregularly observed time series. Our TGNN4I model is designed to handle both irregular time steps and partial observations of the graph. This is achieved by introducing a time-continuous latent state in each node, following a linear Ordinary Differential Equation (ODE) defined by the output of a Gated Recurrent Unit (GRU). The ODE has an explicit solution as a combination of exponential decay and periodic dynamics. Observations in the graph neighborhood are taken into account by integrating graph neural network layers in both the GRU state update and predictive model. The time-continuous dynamics additionally enable the model to make predictions at arbitrary time steps. We propose a loss function that leverages this and allows for training the model for forecasting over different time horizons. Experiments on simulated data and real-world data from traffic and climate modeling validate the usefulness of both the graph structure and time-continuous dynamics in settings with irregular observations.

We study the application of large language models to zero-shot and few-shot classification of tabular data. We prompt the large language model with a serialization of the tabular data to a natural-language string, together with a short description of the classification problem. In the few-shot setting, we fine-tune the large language model using some labeled examples. We evaluate several serialization methods including templates, table-to-text models, and large language models. Despite its simplicity, we find that this technique outperforms prior deep-learning-based tabular classification methods on several benchmark datasets. In most cases, even zero-shot classification obtains non-trivial performance, illustrating the method’s ability to exploit prior knowledge encoded in large language models. Unlike many deep learning methods for tabular datasets, this approach is also competitive with strong traditional baselines like gradient-boosted trees, especially in the very-few-shot setting.

Thompson sampling has become a ubiquitous approach to online decision problems with bandit feedback. The key algorithmic task for Thompson sampling is drawing a sample from the posterior of the optimal action. We propose an alternative arm selection rule we dub TS-UCB, that requires negligible additional computational effort but provides significant performance improvements relative to Thompson sampling. At each step, TS-UCB computes a score for each arm using two ingredients: posterior sample(s) and upper confidence bounds. TS-UCB can be used in any setting where these two quantities are available, and it is flexible in the number of posterior samples it takes as input. TS-UCB achieves materially lower regret on a comprehensive suite of synthetic and real-world datasets, including a personalized article recommendation dataset from Yahoo! and a suite of benchmark datasets from a deep bandit suite proposed in Riquelme et al. (2018). Finally, from a theoretical perspective, we establish optimal regret guarantees for TS-UCB for both the K-armed and linear bandit models.

Clustering time-series data in healthcare is crucial for clinical phenotyping to understand patients’ disease progression patterns and to design treatment guidelines tailored to homogeneous patient subgroups. While rich temporal dynamics enable the discovery of potential clusters beyond static correlations, two major challenges remain outstanding: i) discovery of predictive patterns from many potential temporal correlations in the multi-variate time-series data and ii) association of individual temporal patterns to the target label distribution that best characterizes the underlying clinical progression. To address such challenges, we develop a novel temporal clustering method, T-Phenotype, to discover phenotypes of predictive temporal patterns from labeled time-series data. We introduce an efficient representation learning approach in frequency domain that can encode variable-length, irregularly-sampled time-series into a unified representation space, which is then applied to identify various temporal patterns that potentially contribute to the target label using a new notion of path-based similarity. Throughout the experiments on synthetic and real-world datasets, we show that T-Phenotype achieves the best phenotype discovery performance over all the evaluated baselines. We further demonstrate the utility of T-Phenotype by uncovering clinically meaningful patient subgroups characterized by unique temporal patterns.

Multi-agent interactions are increasingly important in the context of reinforcement learning, and the theoretical foundations of policy gradient methods have attracted surging research interest. We investigate the global convergence of natural policy gradient (NPG) algorithms in multi-agent learning. We first show that vanilla NPG may not have parameter convergence, i.e., the convergence of the vector that parameterizes the policy, even when the payoffs are regularized (which enabled strong convergence guarantees in the policy space in the literature). This non-convergence of parameters leads to stability issues in learning, which becomes especially relevant in the function approximation setting, where we can only operate on low-dimensional parameters, instead of the high-dimensional policy. We then propose variants of the NPG algorithm, for several standard multi-agent learning scenarios: two-player zero-sum matrix and Markov games, and multi-player monotone games, with global last-iterate parameter convergence guarantees. We also generalize the results to certain function approximation settings. Note that in our algorithms, the agents take symmetric roles. Our results might also be of independent interest for solving nonconvex-nonconcave minimax optimization problems with certain structures. Simulations are also provided to corroborate our theoretical findings.

We tackle the cross-modal retrieval problem, where learning is only supervised by the relevant multi-modal pairs in the data. Although the contrastive learning is the most popular approach for this task, it makes potentially wrong assumption that the instances in different pairs are automatically irrelevant. To address the issue, we propose a novel loss function that is based on self-labeling of the unknown semantic classes. Specifically, we aim to predict class labels of the data instances in each modality, and assign those labels to the corresponding instances in the other modality (i.e., swapping the pseudo labels). With these swapped labels, we learn the data embedding for each modality using the supervised cross-entropy loss. This way, cross-modal instances from different pairs that are semantically related can be aligned to each other by the class predictor. We tested our approach on several real-world cross-modal retrieval problems, including text-based video retrieval, sketch-based image retrieval, and image-text retrieval. For all these tasks our method achieves significant performance improvement over the contrastive learning.

Synthetic data is becoming an increasingly promising technology, and successful applications can improve privacy, fairness, and data democratization. While there are many methods for generating synthetic tabular data, the task remains non-trivial and unexplored for specific scenarios. One such scenario is survival data. Here, the key difficulty is censoring: for some instances, we are not aware of the time of event, or if one even occurred. Imbalances in censoring and time horizons cause generative models to experience three new failure modes specific to survival analysis: (1) generating too few at-risk members; (2) generating too many at-risk members; and (3) censoring too early. We formalize these failure modes and provide three new generative metrics to quantify them. Following this, we propose SurvivalGAN, a generative model that handles survival data firstly by addressing the imbalance in the censoring and event horizons, and secondly by using a dedicated mechanism for approximating time-to-event/censoring. We evaluate this method via extensive experiments on medical datasets. SurvivalGAN outperforms multiple baselines at generating survival data, and in particular addresses the failure modes as measured by the new metrics, in addition to improving downstream performance of survival models trained on the synthetic data.

We consider a task of surveillance-evading path-planning in a continuous setting. An Evader strives to escape from a 2D domain while minimizing the risk of detection (and immediate capture). The probability of detection is path-dependent and determined by the spatially inhomogeneous surveillance intensity, which is fixed but a priori unknown and gradually learned in the multi-episodic setting. We introduce a Bayesian reinforcement learning algorithm that relies on a Gaussian Process regression (to model the surveillance intensity function based on the information from prior episodes), numerical methods for Hamilton-Jacobi PDEs (to plan the best continuous trajectories based on the current model), and Confidence Bounds (to balance the exploration vs exploitation). We use numerical experiments and regret metrics to highlight the significant advantages of our approach compared to traditional graph-based algorithms of reinforcement learning.

Learning causal relationships between variables is a fundamental task in causal inference and directed acyclic graphs (DAGs) are a popular choice to represent the causal relationships. As one can recover a causal graph only up to its Markov equivalence class from observations, interventions are often used for the recovery task. Interventions are costly in general and it is important to design algorithms that minimize the number of interventions performed. In this work, we study the problem of identifying the smallest set of interventions required to learn the causal relationships between a subset of edges (target edges). Under the assumptions of faithfulness, causal sufficiency, and ideal interventions, we study this problem in two settings: when the underlying ground truth causal graph is known (subset verification) and when it is unknown (subset search). For the subset verification problem, we provide an efficient algorithm to compute a minimum sized interventional set; we further extend these results to bounded size non-atomic interventions and node-dependent interventional costs. For the subset search problem, in the worst case, we show that no algorithm (even with adaptivity or randomization) can achieve an approximation ratio that is asymptotically better than the vertex cover of the target edges when compared with the subset verification number. This result is surprising as there exists a logarithmic approximation algorithm for the search problem when we wish to recover the whole causal graph. To obtain our results, we prove several interesting structural properties of interventional causal graphs that we believe have applications beyond the subset verification/search problems studied here.

Nonlinear node embedding techniques such as DeepWalk and Node2Vec are used extensively in practice to uncover structure in graphs. Despite theoretical guarantees in special regimes (such as the case of high embedding dimension), the structure of the optimal low dimensional embeddings has not been formally understood even for graphs obtained from simple generative models. We consider the stochastic block model and show that under appropriate separation conditions, the optimal embeddings can be analytically characterized. Akin to known results on eigenvector based (spectral) embeddings, we prove theoretically that solution vectors are well-clustered, up to a sublinear error.

The strong Lottery Ticket Hypothesis (LTH) (Ramanujan et al., 2019; Zhou et al., 2019) claims the existence of a subnetwork in a sufficiently large, randomly initialized neural network that approximates some target neural network without the need of training. We extend the theoretical guarantee of the strong LTH literature to a scenario more similar to the original LTH, by generalizing the weight change in the pre-training step to some perturbation around initialization. In particular, we focus on the following open questions: By allowing an $\varepsilon$-scale perturbation on the random initial weights, can we reduce the over-parameterization requirement for the candidate network in the strong LTH? Furthermore, does the weight change by SGD coincide with a good set of such perturbation? We answer the first question by first extending the theoretical result on subset sum problem (Lueker, 1998) to allow perturbation on the candidates. Applying this result to the neural network setting, we show that by allowing $\varepsilon$-scale perturbation, we can reduce the over-parameterization requirement of the strong LTH by a factor of $O(1/(1+\varepsilon))$. To answer the second question, we show via experiments that the perturbed weight achieved by the projected SGD shows better performance under the strong LTH pruning.

Determining subgroups that respond especially well (or poorly) to specific interventions (medical or policy) requires new supervised learning methods tailored specifically for causal inference. Bayesian Causal Forest (BCF) is a recent method that has been documented to perform well on data generating processes with strong confounding of the sort that is plausible in many applications. This paper develops a novel algorithm for fitting the BCF model, which is more efficient than the previous Gibbs sampler. The new algorithm can be used to initialize independent chains of the existing Gibbs sampler leading to better posterior exploration and coverage of the associated interval estimates in simulation studies. The new algorithm is compared to related approaches via simulation studies as well as an empirical analysis.

Spectral risk objectives – also called L-risks – allow for learning systems to interpolate between optimizing average-case performance (as in empirical risk minimization) and worst-case performance on a task. We develop LSVRG, a stochastic algorithm to optimize these quantities by characterizing their subdifferential and addressing challenges such as biasedness of subgradient estimates and non-smoothness of the objective. We show theoretically and experimentally that out-of-the-box approaches such as stochastic subgradient and dual averaging can be hindered by bias, whereas our approach exhibits linear convergence.