Davin Choo

Davin Choo, Yuval Dagan, Constantinos Daskalakis et al.

We provide time- and sample-efficient algorithms for learning and testing latent-tree Ising models, i.e. Ising models that may only be observed at their leaf nodes. On the learning side, we obtain efficient algorithms for learning a tree-structured Ising model whose leaf node distribution is close in Total Variation Distance, improving on the results of prior work. On the testing side, we provide an efficient algorithm with fewer samples for testing whether two latent-tree Ising models have leaf-node distributions that are close or far in Total Variation distance. We obtain our algorithms by showing novel localization results for the total variation distance between the leaf-node distributions of tree-structured Ising models, in terms of their marginals on pairs of leaves.

Davin Choo, Kirankumar Shiragur, Arnab Bhattacharyya

We study two problems related to recovering causal graphs from interventional data: (i) $\textit{verification}$, where the task is to check if a purported causal graph is correct, and (ii) $\textit{search}$, where the task is to recover the correct causal graph. For both, we wish to minimize the number of interventions performed. For the first problem, we give a characterization of a minimal sized set of atomic interventions that is necessary and sufficient to check the correctness of a claimed causal graph. Our characterization uses the notion of $\textit{covered edges}$, which enables us to obtain simple proofs and also easily reason about earlier known results. We also generalize our results to the settings of bounded size interventions and node-dependent interventional costs. For all the above settings, we provide the first known provable algorithms for efficiently computing (near)-optimal verifying sets on general graphs. For the second problem, we give a simple adaptive algorithm based on graph separators that produces an atomic intervention set which fully orients any essential graph while using $\mathcal{O}(\log n)$ times the optimal number of interventions needed to $\textit{verify}$ (verifying size) the underlying DAG on $n$ vertices. This approximation is tight as $\textit{any}$ search algorithm on an essential line graph has worst case approximation ratio of $Ω(\log n)$ with respect to the verifying size. With bounded size interventions, each of size $\leq k$, our algorithm gives an $\mathcal{O}(\log n \cdot \log k)$ factor approximation. Our result is the first known algorithm that gives a non-trivial approximation guarantee to the verifying size on general unweighted graphs and with bounded size interventions.

Davin Choo, Joy Qiping Yang, Arnab Bhattacharyya et al.

We establish finite-sample guarantees for efficient proper learning of bounded-degree polytrees, a rich class of high-dimensional probability distributions and a subclass of Bayesian networks, a widely-studied type of graphical model. Recently, Bhattacharyya et al. (2021) obtained finite-sample guarantees for recovering tree-structured Bayesian networks, i.e., 1-polytrees. We extend their results by providing an efficient algorithm which learns $d$-polytrees in polynomial time and sample complexity for any bounded $d$ when the underlying undirected graph (skeleton) is known. We complement our algorithm with an information-theoretic sample complexity lower bound, showing that the dependence on the dimension and target accuracy parameters are nearly tight.

Akseli Kangaslahti, Davin Choo, Milind Tambe et al.

Treating and preventing Human Immunodeficiency Virus (HIV) remains a critical global health challenge. While antiretroviral therapy provides a path toward viral suppression -- effectively eliminating an individual's transmission risk -- systemic resource constraints limit the reach of intervention efforts. This work addresses the strategic distribution of intensive resources among virally unsuppressed individuals to minimize the expected cascade of new infections within a transmission network. We formalize this challenge as a novel constrained optimization problem where we have resources to "treat" $k$ out of a set $\mathbf{P}$ of virally unsuppressed individuals, and establish its theoretical connections to existing computational literature. We then propose Cascade-Aware Suppression of Transmission (CAST), a polynomial-time $(δ, ε)$-approximation algorithm that achieves a $2\sqrt{|\mathbf{P}|}$ approximation ratio by leveraging connections to the Minimum-$k$-Union (MkU) problem and Hoeffding-style concentration bounds. Extensive evaluations on real-world HIV networks demonstrate that CAST outperforms standard public health and computer science baselines. Furthermore, we show that CAST is empirically robust across diverse infectious disease networks, varied edge probability initializations, and settings involving imperfect network data.

Davin Choo, Kirankumar Shiragur

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.

Davin Choo, Kirankumar Shiragur

Causal discovery from interventional data is an important problem, where the task is to design an interventional strategy that learns the hidden ground truth causal graph $G(V,E)$ on $|V| = n$ nodes while minimizing the number of performed interventions. Most prior interventional strategies broadly fall into two categories: non-adaptive and adaptive. Non-adaptive strategies decide on a single fixed set of interventions to be performed while adaptive strategies can decide on which nodes to intervene on sequentially based on past interventions. While adaptive algorithms may use exponentially fewer interventions than their non-adaptive counterparts, there are practical concerns that constrain the amount of adaptivity allowed. Motivated by this trade-off, we study the problem of $r$-adaptivity, where the algorithm designer recovers the causal graph under a total of $r$ sequential rounds whilst trying to minimize the total number of interventions. For this problem, we provide a $r$-adaptive algorithm that achieves $O(\min\{r,\log n\} \cdot n^{1/\min\{r,\log n\}})$ approximation with respect to the verification number, a well-known lower bound for adaptive algorithms. Furthermore, for every $r$, we show that our approximation is tight. Our definition of $r$-adaptivity interpolates nicely between the non-adaptive ($r=1$) and fully adaptive ($r=n$) settings where our approximation simplifies to $O(n)$ and $O(\log n)$ respectively, matching the best-known approximation guarantees for both extremes. Our results also extend naturally to the bounded size interventions.

Arnab Bhattacharyya, Davin Choo, Philips George John et al.

Given i.i.d.~samples from an unknown distribution $P$, the goal of distribution learning is to recover the parameters of a distribution that is close to $P$. When $P$ belongs to the class of product distributions on the Boolean hypercube $\{0,1\}^d$, it is known that $Ω(d/\varepsilon^2)$ samples are necessary to learn $P$ within total variation (TV) distance $\varepsilon$. We revisit this problem when the learner is also given as advice the parameters of a product distribution $Q$. We show that there is an efficient algorithm to learn $P$ within TV distance $\varepsilon$ that has sample complexity $\tilde{O}(d^{1-η}/\varepsilon^2)$, if $\|\mathbf{p} - \mathbf{q}\|_1 < \varepsilon d^{0.5 - Ω(η)}$. Here, $\mathbf{p}$ and $\mathbf{q}$ are the mean vectors of $P$ and $Q$ respectively, and no bound on $\|\mathbf{p} - \mathbf{q}\|_1$ is known to the algorithm a priori.

Arnab Bhattacharyya, Davin Choo, Sutanu Gayen et al.

Bayes nets are extensively used in practice to efficiently represent joint probability distributions over a set of random variables and capture dependency relations. In a seminal paper, Chickering et al. (JMLR 2004) showed that given a distribution $\mathbb{P}$, that is defined as the marginal distribution of a Bayes net, it is $\mathsf{NP}$-hard to decide whether there is a parameter-bounded Bayes net that represents $\mathbb{P}$. They called this problem LEARN. In this work, we extend the $\mathsf{NP}$-hardness result of LEARN and prove the $\mathsf{NP}$-hardness of a promise search variant of LEARN, whereby the Bayes net in question is guaranteed to exist and one is asked to find such a Bayes net. We complement our hardness result with a positive result about the sample complexity that is sufficient to recover a parameter-bounded Bayes net that is close (in TV distance) to a given distribution $\mathbb{P}$, that is represented by some parameter-bounded Bayes net, generalizing a degree-bounded sample complexity result of Brustle et al. (EC 2020).

Davin Choo, Themis Gouleakis, Chun Kai Ling et al.

We study the problem of online unweighted bipartite matching with $n$ offline vertices and $n$ online vertices where one wishes to be competitive against the optimal offline algorithm. While the classic RANKING algorithm of Karp et al. [1990] provably attains competitive ratio of $1-1/e > 1/2$, we show that no learning-augmented method can be both 1-consistent and strictly better than $1/2$-robust under the adversarial arrival model. Meanwhile, under the random arrival model, we show how one can utilize methods from distribution testing to design an algorithm that takes in external advice about the online vertices and provably achieves competitive ratio interpolating between any ratio attainable by advice-free methods and the optimal ratio of 1, depending on the advice quality.

Arnab Bhattacharyya, Davin Choo, Philips George John et al.

We revisit the problem of distribution learning within the framework of learning-augmented algorithms. In this setting, we explore the scenario where a probability distribution is provided as potentially inaccurate advice on the true, unknown distribution. Our objective is to develop learning algorithms whose sample complexity decreases as the quality of the advice improves, thereby surpassing standard learning lower bounds when the advice is sufficiently accurate. Specifically, we demonstrate that this outcome is achievable for the problem of learning a multivariate Gaussian distribution $N(\boldsymbolμ, \boldsymbolΣ)$ in the PAC learning setting. Classically, in the advice-free setting, $\tildeΘ(d^2/\varepsilon^2)$ samples are sufficient and worst case necessary to learn $d$-dimensional Gaussians up to TV distance $\varepsilon$ with constant probability. When we are additionally given a parameter $\tilde{\boldsymbolΣ}$ as advice, we show that $\tilde{O}(d^{2-β}/\varepsilon^2)$ samples suffices whenever $\| \tilde{\boldsymbolΣ}^{-1/2} \boldsymbolΣ \tilde{\boldsymbolΣ}^{-1/2} - \boldsymbol{I_d} \|_1 \leq \varepsilon d^{1-β}$ (where $\|\cdot\|_1$ denotes the entrywise $\ell_1$ norm) for any $β> 0$, yielding a polynomial improvement over the advice-free setting.

Davin Choo, Kirankumar Shiragur, Caroline Uhler

Causal graph discovery is a significant problem with applications across various disciplines. However, with observational data alone, the underlying causal graph can only be recovered up to its Markov equivalence class, and further assumptions or interventions are necessary to narrow down the true graph. This work addresses the causal discovery problem under the setting of stochastic interventions with the natural goal of minimizing the number of interventions performed. We propose the following stochastic intervention model which subsumes existing adaptive noiseless interventions in the literature while capturing scenarios such as fat-hand interventions and CRISPR gene knockouts: any intervention attempt results in an actual intervention on a random subset of vertices, drawn from a distribution dependent on attempted action. Under this model, we study the two fundamental problems in causal discovery of verification and search and provide approximation algorithms with polylogarithmic competitive ratios and provide some preliminary experimental results.

Davin Choo, Billy Jin, Yongho Shin

Online bipartite matching is a fundamental problem in online optimization, extensively studied both in its integral and fractional forms due to its theoretical significance and practical applications, such as online advertising and resource allocation. Motivated by recent progress in learning-augmented algorithms, we study online bipartite fractional matching when the algorithm is given advice in the form of a suggested matching in each iteration. We develop algorithms for both the vertex-weighted and unweighted variants that provably dominate the naive "coin flip" strategy of randomly choosing between the advice-following and advice-free algorithms. Moreover, our algorithm for the vertex-weighted setting extends to the AdWords problem under the small bids assumption, yielding a significant improvement over the seminal work of Mahdian, Nazerzadeh, and Saberi (EC 2007, TALG 2012). Complementing our positive results, we establish a hardness bound on the robustness-consistency tradeoff that is attainable by any algorithm. We empirically validate our algorithms through experiments on synthetic and real-world data.

Davin Choo, Yuqi Pan, Tonghan Wang et al.

We study a sequential decision-making problem on a $n$-node graph $\mathcal{G}$ where each node has an unknown label from a finite set $\mathbfΩ$, drawn from a joint distribution $\mathcal{P}$ that is Markov with respect to $\mathcal{G}$. At each step, selecting a node reveals its label and yields a label-dependent reward. The goal is to adaptively choose nodes to maximize expected accumulated discounted rewards. We impose a frontier exploration constraint, where actions are limited to neighbors of previously selected nodes, reflecting practical constraints in settings such as contact tracing and robotic exploration. We design a Gittins index-based policy that applies to general graphs and is provably optimal when $\mathcal{G}$ is a forest. Our implementation runs in $\mathcal{O}(n^2 \cdot |\mathbfΩ|^2)$ time while using $\mathcal{O}(n \cdot |\mathbfΩ|^2)$ oracle calls to $\mathcal{P}$ and $\mathcal{O}(n^2 \cdot |\mathbfΩ|)$ space. Experiments on synthetic and real-world graphs show that our method consistently outperforms natural baselines, including in non-tree, budget-limited, and undiscounted settings. For example, in HIV testing simulations on real-world sexual interaction networks, our policy detects nearly all positive cases with only half the population tested, substantially outperforming other baselines.

Davin Choo, Themis Gouleakis, Arnab Bhattacharyya

We introduce the problem of active causal structure learning with advice. In the typical well-studied setting, the learning algorithm is given the essential graph for the observational distribution and is asked to recover the underlying causal directed acyclic graph (DAG) $G^*$ while minimizing the number of interventions made. In our setting, we are additionally given side information about $G^*$ as advice, e.g. a DAG $G$ purported to be $G^*$. We ask whether the learning algorithm can benefit from the advice when it is close to being correct, while still having worst-case guarantees even when the advice is arbitrarily bad. Our work is in the same space as the growing body of research on algorithms with predictions. When the advice is a DAG $G$, we design an adaptive search algorithm to recover $G^*$ whose intervention cost is at most $O(\max\{1, \log ψ\})$ times the cost for verifying $G^*$; here, $ψ$ is a distance measure between $G$ and $G^*$ that is upper bounded by the number of variables $n$, and is exactly 0 when $G=G^*$. Our approximation factor matches the state-of-the-art for the advice-less setting.

Davin Choo, Kirankumar Shiragur

Recovering causal relationships from data is an important problem. Using observational data, one can typically only recover causal graphs up to a Markov equivalence class and additional assumptions or interventional data are needed for complete recovery. In this work, under some standard assumptions, we study causal graph discovery via adaptive interventions with node-dependent interventional costs. For this setting, we show that no algorithm can achieve an approximation guarantee that is asymptotically better than linear in the number of vertices with respect to the verification number; a well-established benchmark for adaptive search algorithms. Motivated by this negative result, we define a new benchmark that captures the worst-case interventional cost for any search algorithm. Furthermore, with respect to this new benchmark, we provide adaptive search algorithms that achieve logarithmic approximations under various settings: atomic, bounded size interventions and generalized cost objectives.

Arnab Bhattacharyya, Davin Choo, Rishikesh Gajjala et al.

Gaussian Bayesian networks (a.k.a. linear Gaussian structural equation models) are widely used to model causal interactions among continuous variables. In this work, we study the problem of learning a fixed-structure Gaussian Bayesian network up to a bounded error in total variation distance. We analyze the commonly used node-wise least squares regression (LeastSquares) and prove that it has a near-optimal sample complexity. We also study a couple of new algorithms for the problem: - BatchAvgLeastSquares takes the average of several batches of least squares solutions at each node, so that one can interpolate between the batch size and the number of batches. We show that BatchAvgLeastSquares also has near-optimal sample complexity. - CauchyEst takes the median of solutions to several batches of linear systems at each node. We show that the algorithm specialized to polytrees, CauchyEstTree, has near-optimal sample complexity. Experimentally, we show that for uncontaminated, realizable data, the LeastSquares algorithm performs best, but in the presence of contamination or DAG misspecification, CauchyEst/CauchyEstTree and BatchAvgLeastSquares respectively perform better.

Davin Choo, Tommaso d'Orsi

We study the problem of sparse tensor principal component analysis: given a tensor $\pmb Y = \pmb W + λx^{\otimes p}$ with $\pmb W \in \otimes^p\mathbb{R}^n$ having i.i.d. Gaussian entries, the goal is to recover the $k$-sparse unit vector $x \in \mathbb{R}^n$. The model captures both sparse PCA (in its Wigner form) and tensor PCA. For the highly sparse regime of $k \leq \sqrt{n}$, we present a family of algorithms that smoothly interpolates between a simple polynomial-time algorithm and the exponential-time exhaustive search algorithm. For any $1 \leq t \leq k$, our algorithms recovers the sparse vector for signal-to-noise ratio $λ\geq \tilde{\mathcal{O}} (\sqrt{t} \cdot (k/t)^{p/2})$ in time $\tilde{\mathcal{O}}(n^{p+t})$, capturing the state-of-the-art guarantees for the matrix settings (in both the polynomial-time and sub-exponential time regimes). Our results naturally extend to the case of $r$ distinct $k$-sparse signals with disjoint supports, with guarantees that are independent of the number of spikes. Even in the restricted case of sparse PCA, known algorithms only recover the sparse vectors for $λ\geq \tilde{\mathcal{O}}(k \cdot r)$ while our algorithms require $λ\geq \tilde{\mathcal{O}}(k)$. Finally, by analyzing the low-degree likelihood ratio, we complement these algorithmic results with rigorous evidence illustrating the trade-offs between signal-to-noise ratio and running time. This lower bound captures the known lower bounds for both sparse PCA and tensor PCA. In this general model, we observe a more intricate three-way trade-off between the number of samples $n$, the sparsity $k$, and the tensor power $p$.

Jing Lim, Joshua Wong, Minn Xuan Wong et al.

Chemical structure elucidation is a serious bottleneck in analytical chemistry today. We address the problem of identifying an unknown chemical threat given its mass spectrum and its chemical formula, a task which might take well trained chemists several days to complete. Given a chemical formula, there could be over a million possible candidate structures. We take a data driven approach to rank these structures by using neural networks to predict the presence of substructures given the mass spectrum, and matching these substructures to the candidate structures. Empirically, we evaluate our approach on a data set of chemical agents built for unknown chemical threat identification. We show that our substructure classifiers can attain over 90% micro F1-score, and we can find the correct structure among the top 20 candidates in 88% and 71% of test cases for two compound classes.