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Register a new userQuantifying Model Complexity via Functional Decomposition for Better Post-Hoc Interpretability
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Post-hoc model-agnostic interpretation methods such as partial dependence plots can be employed to interpret complex machine learning models. While these interpretation methods can be applied regardless of model complexity, they can produce misleading and verbose results if the model is too complex, especially w.r.t. feature interactions. To quantify the complexity of arbitrary machine learning models, we propose model-agnostic complexity measures based on functional decomposition: number of features used, interaction strength and main effect complexity. We show that post-hoc interpretation of models that minimize the three measures is more reliable and compact. Furthermore, we demonstrate the application of these measures in a multi-objective optimization approach which simultaneously minimizes loss and complexity.
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Natural Language Processing (NLP) models have become increasingly more complex and widespread. With recent developments in neural networks, a growing concern is whether it is responsible to use these models. Concerns such as safety and ethics can be partially addressed by providing explanations. Furthermore, when models do fail, providing explanations is paramount for accountability purposes. To this end, interpretability serves to provide these explanations in terms that are understandable to humans. Central to what is understandable is how explanations are communicated. Therefore, this survey provides a categorization of how recent interpretability methods communicate explanations and discusses the methods in depth. Furthermore, the survey focuses on post-hoc methods, which provide explanations after a model is learned and generally model-agnostic. A common concern for this class of methods is whether they accurately reflect the model. Hence, how these post-hoc methods are evaluated is discussed throughout the paper.
Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize them, and in the past regularization has mostly been performed using bespoke modifications to the algorithms, tailored for the particular form of the desired regularizer. We present a general method of regularizing tensor decomposition methods which can be used for any likelihood model that is learnable using tensor decomposition methods and any differentiable regularization function by supplementing the training data with pseudo-data. The pseudo-data is optimized to balance two terms: being as close as possible to the true data and enforcing the desired regularization. On synthetic, semi-synthetic and real data, we demonstrate that our method can improve inference accuracy and regularize for a broad range of goals including transfer learning, sparsity, interpretability, and orthogonality of the learned parameters.
We consider the problem of model selection for two popular stochastic linear bandit settings, and propose algorithms that adapts to the unknown problem complexity. In the first setting, we consider the $K$ armed mixture bandits, where the mean reward of arm $i in [K]$, is $mu_i+ langle alpha_{i,t},theta^* rangle $, with $alpha_{i,t} in mathbb{R}^d$ being the known context vector and $mu_i in [-1,1]$ and $theta^*$ are unknown parameters. We define $|theta^*|$ as the problem complexity and consider a sequence of nested hypothesis classes, each positing a different upper bound on $|theta^*|$. Exploiting this, we propose Adaptive Linear Bandit (ALB), a novel phase based algorithm that adapts to the true problem complexity, $|theta^*|$. We show that ALB achieves regret scaling of $O(|theta^*|sqrt{T})$, where $|theta^*|$ is apriori unknown. As a corollary, when $theta^*=0$, ALB recovers the minimax regret for the simple bandit algorithm without such knowledge of $theta^*$. ALB is the first algorithm that uses parameter norm as model section criteria for linear bandits. Prior state of art algorithms cite{osom} achieve a regret of $O(Lsqrt{T})$, where $L$ is the upper bound on $|theta^*|$, fed as an input to the problem. In the second setting, we consider the standard linear bandit problem (with possibly an infinite number of arms) where the sparsity of $theta^*$, denoted by $d^* leq d$, is unknown to the algorithm. Defining $d^*$ as the problem complexity, we show that ALB achieves $O(d^*sqrt{T})$ regret, matching that of an oracle who knew the true sparsity level. This methodology is then extended to the case of finitely many arms and similar results are proven. This is the first algorithm that achieves such model selection guarantees. We further verify our results via synthetic and real-data experiments.
We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but requires only basic algebra and probability theory to understand and verify. The theoretical concepts presented are well-studied, primarily in the statistics literature. The goal of this paper is to advocate their wider adoption for performance evaluation in empirical machine learning.
We discuss structured Schatten norms for tensor decomposition that includes two recently proposed norms (overlapped and latent) for convex-optimization-based tensor decomposition, and connect tensor decomposition with wider literature on structured sparsity. Based on the properties of the structured Schatten norms, we mathematically analyze the performance of latent approach for tensor decomposition, which was empirically found to perform better than the overlapped approach in some settings. We show theoretically that this is indeed the case. In particular, when the unknown true tensor is low-rank in a specific mode, this approach performs as good as knowing the mode with the smallest rank. Along the way, we show a novel duality result for structures Schatten norms, establish the consistency, and discuss the identifiability of this approach. We confirm through numerical simulations that our theoretical prediction can precisely predict the scaling behavior of the mean squared error.
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