More Like this

1. Sparse semiparametric canonical correlation analysis for data of mixed types

   https://doi.org/10.1093/biomet/asaa007  

   Yoon, Grace; Carroll, Raymond J; Gaynanova, Irina (April 2020, Biometrika)

   Summary Canonical correlation analysis investigates linear relationships between two sets of variables, but it often works poorly on modern datasets because of high dimensionality and mixed data types such as continuous, binary and zero-inflated. To overcome these challenges, we propose a semiparametric approach to sparse canonical correlation analysis based on the Gaussian copula. The main result of this paper is a truncated latent Gaussian copula model for data with excess zeros, which allows us to derive a rank-based estimator of the latent correlation matrix for mixed variable types without estimation of marginal transformation functions. The resulting canonical correlation analysis method works well in high-dimensional settings, as demonstrated via numerical studies, and when applied to the analysis of association between gene expression and microRNA data from breast cancer patients. 

   more » « less
2. A mutual information criterion with applications to canonical correlation analysis and graphical models.

   https://doi.org/10.1002/sta4.385  

   DelSole, Timothy; Tippett, Michael K. (April 2021, Stat)

   This paper derives a criterion for deciding conditional independence that is consistent with small-sample corrections of Akaike's information criterion but is easier to apply to such problems as selecting variables in canonical correlation analysis and selecting graphical models. The criterion reduces to mutual information when the assumed distribution equals the true distribution; hence, it is called mutual information criterion (MIC). Although small-sample Kullback–Leibler criteria for these selection problems have been proposed previously, some of which are not widely known, MIC is strikingly more direct to derive and apply. 

   more » « less
3. Max-sliced mutual information

   Tsur, Dor; Goldfeld, Ziv; Greenewald, Kristjan (February 2024, Advances in neural information processing systems)

   Quantifying dependence between high-dimensional random variables is central to statistical learning and inference. Two classical methods are canonical correlation analysis (CCA), which identifies maximally correlated projected versions of the original variables, and Shannon's mutual information, which is a universal dependence measure that also captures high-order dependencies. However, CCA only accounts for linear dependence, which may be insufficient for certain applications, while mutual information is often infeasible to compute/estimate in high dimensions. This work proposes a middle ground in the form of a scalable information-theoretic generalization of CCA, termed max-sliced mutual information (mSMI). mSMI equals the maximal mutual information between low-dimensional projections of the high-dimensional variables, which reduces back to CCA in the Gaussian case. It enjoys the best of both worlds: capturing intricate dependencies in the data while being amenable to fast computation and scalable estimation from samples. We show that mSMI retains favorable structural properties of Shannon's mutual information, like variational forms and identification of independence. We then study statistical estimation of mSMI, propose an efficiently computable neural estimator, and couple it with formal non-asymptotic error bounds. We present experiments that demonstrate the utility of mSMI for several tasks, encompassing independence testing, multi-view representation learning, algorithmic fairness, and generative modeling. We observe that mSMI consistently outperforms competing methods with little-to-no computational overhead. 

   more » « less
4. LpBound : Pessimistic Cardinality Estimation Using ℓ _p -Norms of Degree Sequences

   https://doi.org/10.1145/3725321  

   Zhang, Haozhe; Mayer, Christoph; Abo_Khamis, Mahmoud; Olteanu, Dan; Suciu, Dan (June 2025, Proceedings of the ACM on Management of Data)

   Cardinality estimation is the problem of estimating the size of the output of a query, without actually evaluating the query. The cardinality estimator is a critical piece of a query optimizer, and is often the main culprit when the optimizer chooses a poor plan. This paper introduces LpBound, a pessimistic cardinality estimator for multi-join queries (acyclic or cyclic) with selection predicates and group-by clauses.LpBoundcomputes a guaranteed upper bound on the size of the query output using simple statistics on the input relations, consisting of ℓ_p-norms of degree sequences. The bound is the optimal solution of a linear program whose constraints encode data statistics and Shannon inequalities. We introduce two optimizations that exploit the structure of the query in order to speed up the estimation time and makeLpBoundpractical. We experimentally evaluateLpBoundagainst a range of traditional, pessimistic, and machine learning-based estimators on the JOB, STATS, and subgraph matching benchmarks. Our main finding is thatLpBoundcan be orders of magnitude more accurate than traditional estimators used in mainstream open-source and commercial database systems. Yet it has comparable low estimation time and space requirements. When injected the estimates ofLpBound, Postgres derives query plans at least as good as those derived using the true cardinalities. 

   more » « less
5. More efficient approximation of smoothing splines via space-filling basis selection

   https://doi.org/10.1093/biomet/asaa019  

   Meng, Cheng; Zhang, Xinlian; Zhang, Jingyi; Zhong, Wenxuan; Ma, Ping (May 2020, Biometrika)

   null (Ed.)

   Summary We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $$n$$, the smoothing spline estimator can be expressed as a linear combination of $$n$$ basis functions, requiring $O(n^3)$ computational time when the number $$d$$ of predictors is two or more. Such a sizeable computational cost hinders the broad applicability of smoothing splines. In practice, the full-sample smoothing spline estimator can be approximated by an estimator based on $$q$$ randomly selected basis functions, resulting in a computational cost of $O(nq^2)$. It is known that these two estimators converge at the same rate when $$q$$ is of order $$O\{n^{2/(pr+1)}\}$$, where $$p\in [1,2]$$ depends on the true function and $r > 1$ depends on the type of spline. Such a $$q$$ is called the essential number of basis functions. In this article, we develop a more efficient basis selection method. By selecting basis functions corresponding to approximately equally spaced observations, the proposed method chooses a set of basis functions with great diversity. The asymptotic analysis shows that the proposed smoothing spline estimator can decrease $$q$$ to around $$O\{n^{1/(pr+1)}\}$$ when $$d\leq pr+1$$. Applications to synthetic and real-world datasets show that the proposed method leads to a smaller prediction error than other basis selection methods. 

   more » « less