Related papers: Optimal estimation of Gaussian (poly)trees
We provide a complete description of possible covariance matrices consistent with a Gaussian latent tree model for any tree. We then present techniques for utilising these constraints to assess whether observed data is compatible with that…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…
The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly polynomial time…
Decision trees are widely used due to their interpretability and efficiency, but they struggle in regression tasks that require reliable extrapolation and well-calibrated uncertainty. Piecewise-constant leaf predictions are bounded by the…
We present a fairly general framework for reducing $(\varepsilon, \delta)$ differentially private (DP) statistical estimation to its non-private counterpart. As the main application of this framework, we give a polynomial time and…
This paper uses Gaussian mixture model instead of linear Gaussian model to fit the distribution of every node in Bayesian network. We will explain why and how we use Gaussian mixture models in Bayesian network. Meanwhile we propose a new…
We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each…
Decision trees built with data remain in widespread use for nonparametric prediction. Predicting probability distributions is preferred over point predictions when uncertainty plays a prominent role in analysis and decision-making. We study…
In many risk-aware and multi-objective reinforcement learning settings, the utility of the user is derived from a single execution of a policy. In these settings, making decisions based on the average future returns is not suitable. For…
We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms. To illustrate our techniques, we…
We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
Significant advances have been made recently on training neural networks, where the main challenge is in solving an optimization problem with abundant critical points. However, existing approaches to address this issue crucially rely on a…
Nonlinear metrics, such as the F1-score, Matthews correlation coefficient, and Fowlkes-Mallows index, are often used to evaluate the performance of machine learning models, in particular, when facing imbalanced datasets that contain more…
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…
Retrieving relevant targets from an extremely large target set under computational limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves of a tree with trainable…
Herein, we investigate the zero-error randomized complexity, which is the least cost against the worst input, of AND-OR tree computation by imposing various restrictions on the algorithm to find the Boolean value of the root of that tree…
We study the problem, introduced by Qiao and Valiant, of learning from untrusted batches. Here, we assume $m$ users, all of whom have samples from some underlying distribution $p$ over $1, \ldots, n$. Each user sends a batch of $k$ i.i.d.…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…