We consider general Gaussian latent tree models in which the observed variables are not restricted to be leaves of the tree. Extending related recent work, we give a full semi-algebraic description of the set of covariance matrices of any such model. In other words, we find polynomial constraints that characterize when a matrix is the covariance matrix of a distribution in a given latent tree model. However, leveraging these constraints to test a given such model is often complicated by the number of constraints being large and by singularities of individual polynomials, which may invalidate standard approximations to relevant probability distributions. Illustrating with the star tree, we propose a new testing methodology that circumvents singularity issues by trading off some statistical estimation efficiency and handles cases with many constraints through recent advances on Gaussian approximation for maxima of sums of high-dimensional random vectors. Our test avoids the need to maximize the possibly multimodal likelihood function of such models and is applicable to models with larger number of variables. These points are illustrated in numerical experiments.

As AI models become ubiquitous in our daily lives, there has been an increasing demand for transparency in ML services. However, the model owner does not want to reveal the weights, as they are considered trade secrets. To solve this problem, researchers have turned to zero-knowledge proofs of ML model inference. These proofs convince the user that the ML model output is correct, without revealing the weights of the model to the user. Past work on these provers can be placed into two categories. The first method compiles the ML model into a low-level circuit, and proves the circuit using a ZK-SNARK. The second method uses custom cryptographic protocols designed only for a specific class of models. Unfortunately, the first method is highly inefficient, making it impractical for the large models used today, and the second method does not generalize well, making it difficult to update in the rapidly changing field of machine learning. To solve this, we propose ZKTorch, an open source end-to-end proving system that compiles ML models into base cryptographic operations called basic blocks, each proved using specialized protocols. ZKTorch is built on top of a novel parallel extension to the Mira accumulation scheme, enabling succinct proofs with minimal accumulation overhead. These contributions allow ZKTorch to achieve at least a $3\times$ reduction in the proof size compared to specialized protocols and up to a $6\times$ speedup in proving time over a general-purpose ZKML framework.

Paper Summary: The paper presents a technique for testing whether a given set of samples are drawn from a postulated Gaussian latent tree model or a saturated Gaussian graphical model. The paper first characterizes a set of necessary and sufficient constraints that any covariance matrix of a Gaussian latent tree model should satisfy. It then uses these constraints to come up with a test statistic. The paper extends past work on testing for Gaussian latent tree models to settings where the observed variables are allowed to have degree up to 2. The test statistic presented in the paper is based on gaussian approximation for maxima of high dimensional sums. Simulations suggest that the test statistic can potentially work in high dimensional settings.

We consider general Gaussian latent tree models in which the observed variables are not restricted to be leaves of the tree. Extending related recent work, we give a full semi-algebraic description of the set of covariance matrices of any such model. In other words, we find polynomial constraints that characterize when a matrix is the covariance matrix of a distribution in a given latent tree model. However, leveraging these constraints to test a given such model is often complicated by the number of constraints being large and by singularities of individual polynomials, which may invalidate standard approximations to relevant probability distributions. Illustrating with the star tree, we propose a new testing methodology that circumvents singularity issues by trading off some statistical estimation efficiency and handles cases with many constraints through recent advances on Gaussian approximation for maxima of sums of high-dimensional random vectors. Our test avoids the need to maximize the possibly multimodal likelihood function of such models and is applicable to models with larger number of variables.