Bin Yu

Abhineet Agarwal, Ana M. Kenney, Yan Shuo Tan et al. · berkeley

Random forests (RFs) are among the most popular supervised learning algorithms due to their nonlinear flexibility and ease-of-use. However, as black box models, they can only be interpreted via algorithmically-defined feature importance methods, such as Mean Decrease in Impurity (MDI), which have been observed to be highly unstable and have ambiguous scientific meaning. Furthermore, they can perform poorly in the presence of smooth or additive structure. To address this, we reinterpret decision trees and MDI as linear regression and $R^2$ values, respectively, with respect to engineered features associated with the tree's decision splits. This allows us to combine the respective strengths of RFs and generalized linear models in a framework called RF+, which also yields an improved feature importance method we call MDI+. Through extensive data-inspired simulations and real-world datasets, we show that RF+ improves prediction accuracy over RFs and that MDI+ outperforms popular feature importance measures in identifying signal features, often yielding more than a 10% improvement over its closest competitor. In case studies on drug response prediction and breast cancer subtyping, we further show that MDI+ extracts well-established genes with significantly greater stability compared to existing feature importance measures.

Aliyah R. Hsu, Georgia Zhou, Yeshwanth Cherapanamjeri et al.

Automated mechanistic interpretation research has attracted great interest due to its potential to scale explanations of neural network internals to large models. Existing automated circuit discovery work relies on activation patching or its approximations to identify subgraphs in models for specific tasks (circuits). They often suffer from slow runtime, approximation errors, and specific requirements of metrics, such as non-zero gradients. In this work, we introduce contextual decomposition for transformers (CD-T) to build interpretable circuits in large language models. CD-T can produce circuits of arbitrary level of abstraction, and is the first able to produce circuits as fine-grained as attention heads at specific sequence positions efficiently. CD-T consists of a set of mathematical equations to isolate contribution of model features. Through recursively computing contribution of all nodes in a computational graph of a model using CD-T followed by pruning, we are able to reduce circuit discovery runtime from hours to seconds compared to state-of-the-art baselines. On three standard circuit evaluation datasets (indirect object identification, greater-than comparisons, and docstring completion), we demonstrate that CD-T outperforms ACDC and EAP by better recovering the manual circuits with an average of 97% ROC AUC under low runtimes. In addition, we provide evidence that faithfulness of CD-T circuits is not due to random chance by showing our circuits are 80% more faithful than random circuits of up to 60% of the original model size. Finally, we show CD-T circuits are able to perfectly replicate original models' behavior (faithfulness $ = 1$) using fewer nodes than the baselines for all tasks. Our results underscore the great promise of CD-T for efficient automated mechanistic interpretability, paving the way for new insights into the workings of large language models.

Tucker Stewart, Bin Yu, Anderson Nascimento et al. · uw

For network administration and maintenance, it is critical to anticipate when networks will receive peak volumes of traffic so that adequate resources can be allocated to service requests made to servers. In the event that sufficient resources are not allocated to servers, they can become prone to failure and security breaches. On the contrary, we would waste a lot of resources if we always allocate the maximum amount of resources. Therefore, anticipating peak volumes in network traffic becomes an important problem. However, popular forecasting models such as Autoregressive Integrated Moving Average (ARIMA) forecast time-series data generally, thus lack in predicting peak volumes in these time-series. More than often, a time-series is a combination of different features, which may include but are not limited to 1) Trend, the general movement of the traffic volume, 2) Seasonality, the patterns repeated over some time periods (e.g. daily and monthly), and 3) Noise, the random changes in the data. Considering that the fluctuation of seasonality can be harmful for trend and peak prediction, we propose to extract seasonalities to facilitate the peak volume predictions in the time domain. The experiments on both synthetic and real network traffic data demonstrate the effectiveness of the proposed method.

Aaron J. Li, Robin Netzorg, Zhihan Cheng et al.

In recent years, work has gone into developing deep interpretable methods for image classification that clearly attributes a model's output to specific features of the data. One such of these methods is the Prototypical Part Network (ProtoPNet), which attempts to classify images based on meaningful parts of the input. While this architecture is able to produce visually interpretable classifications, it often learns to classify based on parts of the image that are not semantically meaningful. To address this problem, we propose the Reward Reweighing, Reselecting, and Retraining (R3) post-processing framework, which performs three additional corrective updates to a pretrained ProtoPNet in an offline and efficient manner. The first two steps involve learning a reward model based on collected human feedback and then aligning the prototypes with human preferences. The final step is retraining, which realigns the base features and the classifier layer of the original model with the updated prototypes. We find that our R3 framework consistently improves both the interpretability and the predictive accuracy of ProtoPNet and its variants.

Jingfeng Wu, Peter L. Bartlett, Matus Telgarsky et al. · berkeley

We consider gradient descent (GD) with a constant stepsize applied to logistic regression with linearly separable data, where the constant stepsize $η$ is so large that the loss initially oscillates. We show that GD exits this initial oscillatory phase rapidly -- in $\mathcal{O}(η)$ steps -- and subsequently achieves an $\tilde{\mathcal{O}}(1 / (ηt) )$ convergence rate after $t$ additional steps. Our results imply that, given a budget of $T$ steps, GD can achieve an accelerated loss of $\tilde{\mathcal{O}}(1/T^2)$ with an aggressive stepsize $η:= Θ( T)$, without any use of momentum or variable stepsize schedulers. Our proof technique is versatile and also handles general classification loss functions (where exponential tails are needed for the $\tilde{\mathcal{O}}(1/T^2)$ acceleration), nonlinear predictors in the neural tangent kernel regime, and online stochastic gradient descent (SGD) with a large stepsize, under suitable separability conditions.

Jingfeng Wu, Peter Bartlett, Matus Telgarsky et al. · berkeley

In overparameterized logistic regression, gradient descent (GD) iterates diverge in norm while converging in direction to the maximum $\ell_2$-margin solution -- a phenomenon known as the implicit bias of GD. This work investigates additional regularization effects induced by early stopping in well-specified high-dimensional logistic regression. We first demonstrate that the excess logistic risk vanishes for early-stopped GD but diverges to infinity for GD iterates at convergence. This suggests that early-stopped GD is well-calibrated, whereas asymptotic GD is statistically inconsistent. Second, we show that to attain a small excess zero-one risk, polynomially many samples are sufficient for early-stopped GD, while exponentially many samples are necessary for any interpolating estimator, including asymptotic GD. This separation underscores the statistical benefits of early stopping in the overparameterized regime. Finally, we establish nonasymptotic bounds on the norm and angular differences between early-stopped GD and $\ell_2$-regularized empirical risk minimizer, thereby connecting the implicit regularization of GD with explicit $\ell_2$-regularization.

Jingfeng Wu, Peter L. Bartlett, Jason D. Lee et al.

Existing theory suggests that for linear regression problems categorized by capacity and source conditions, gradient descent (GD) is always minimax optimal, while both ridge regression and online stochastic gradient descent (SGD) are polynomially suboptimal for certain categories of such problems. Moving beyond minimax theory, this work provides instance-wise comparisons of the finite-sample risks for these algorithms on any well-specified linear regression problem. Our analysis yields three key findings. First, GD dominates ridge regression: with comparable regularization, the excess risk of GD is always within a constant factor of ridge, but ridge can be polynomially worse even when tuned optimally. Second, GD is incomparable with SGD. While it is known that for certain problems GD can be polynomially better than SGD, the reverse is also true: we construct problems, inspired by benign overfitting theory, where optimally stopped GD is polynomially worse. Finally, GD dominates SGD for a significant subclass of problems -- those with fast and continuously decaying covariance spectra -- which includes all problems satisfying the standard capacity condition.

Haotian Li, Rui Zhang, Lingzhi Wang et al.

Recent advances in knowledge graph completion (KGC) have emphasized text-based approaches to navigate the inherent complexities of large-scale knowledge graphs (KGs). While these methods have achieved notable progress, they frequently struggle to fully incorporate the global structural properties of the graph. Stochastic blockmodels (SBMs), especially the latent feature relational model (LFRM), offer robust probabilistic frameworks for identifying latent community structures and improving link prediction. This paper presents a novel probabilistic KGC framework utilizing sparse latent feature models, optimized via a deep variational autoencoder (VAE). Our proposed method dynamically integrates global clustering information with local textual features to effectively complete missing triples, while also providing enhanced interpretability of the underlying latent structures. Extensive experiments on four benchmark datasets with varying scales demonstrate the significant performance gains achieved by our method.

Yu Wang, Siqi Wu, Bin Yu

We study the problem of globally recovering a dictionary from a set of signals via $\ell_1$-minimization. We assume that the signals are generated as i.i.d. random linear combinations of the $K$ atoms from a complete reference dictionary $D^*\in \mathbb R^{K\times K}$, where the linear combination coefficients are from either a Bernoulli type model or exact sparse model. First, we obtain a necessary and sufficient norm condition for the reference dictionary $D^*$ to be a sharp local minimum of the expected $\ell_1$ objective function. Our result substantially extends that of Wu and Yu (2015) and allows the combination coefficient to be non-negative. Secondly, we obtain an explicit bound on the region within which the objective value of the reference dictionary is minimal. Thirdly, we show that the reference dictionary is the unique sharp local minimum, thus establishing the first known global property of $\ell_1$-minimization dictionary learning. Motivated by the theoretical results, we introduce a perturbation-based test to determine whether a dictionary is a sharp local minimum of the objective function. In addition, we also propose a new dictionary learning algorithm based on Block Coordinate Descent, called DL-BCD, which is guaranteed to have monotonic convergence. Simulation studies show that DL-BCD has competitive performance in terms of recovery rate compared to many state-of-the-art dictionary learning algorithms.

Karl Kumbier, Sumanta Basu, Erwin Frise et al.

Standard ChIP-seq peak calling pipelines seek to differentiate biochemically reproducible signals of individual genomic elements from background noise. However, reproducibility alone does not imply functional regulation (e.g., enhancer activation, alternative splicing). Here we present a general-purpose, interpretable machine learning method: signed iterative random forests (siRF), which we use to infer regulatory interactions among transcription factors and functional binding signatures surrounding enhancer elements in Drosophila melanogaster.

Siqi Wu, Bin Yu

We study the theoretical properties of learning a dictionary from $N$ signals $\mathbf x_i\in \mathbb R^K$ for $i=1,...,N$ via $l_1$-minimization. We assume that $\mathbf x_i$'s are $i.i.d.$ random linear combinations of the $K$ columns from a complete (i.e., square and invertible) reference dictionary $\mathbf D_0 \in \mathbb R^{K\times K}$. Here, the random linear coefficients are generated from either the $s$-sparse Gaussian model or the Bernoulli-Gaussian model. First, for the population case, we establish a sufficient and almost necessary condition for the reference dictionary $\mathbf D_0$ to be locally identifiable, i.e., a local minimum of the expected $l_1$-norm objective function. Our condition covers both sparse and dense cases of the random linear coefficients and significantly improves the sufficient condition by Gribonval and Schnass (2010). In addition, we show that for a complete $μ$-coherent reference dictionary, i.e., a dictionary with absolute pairwise column inner-product at most $μ\in[0,1)$, local identifiability holds even when the random linear coefficient vector has up to $O(μ^{-2})$ nonzeros on average. Moreover, our local identifiability results also translate to the finite sample case with high probability provided that the number of signals $N$ scales as $O(K\log K)$.

Geoffrey Schiebinger, Martin J. Wainwright, Bin Yu

Clustering of data sets is a standard problem in many areas of science and engineering. The method of spectral clustering is based on embedding the data set using a kernel function, and using the top eigenvectors of the normalized Laplacian to recover the connected components. We study the performance of spectral clustering in recovering the latent labels of i.i.d. samples from a finite mixture of nonparametric distributions. The difficulty of this label recovery problem depends on the overlap between mixture components and how easily a mixture component is divided into two nonoverlapping components. When the overlap is small compared to the indivisibility of the mixture components, the principal eigenspace of the population-level normalized Laplacian operator is approximately spanned by the square-root kernelized component densities. In the finite sample setting, and under the same assumption, embedded samples from different components are approximately orthogonal with high probability when the sample size is large. As a corollary we control the fraction of samples mislabeled by spectral clustering under finite mixtures with nonparametric components.

Antony Joseph, Bin Yu

The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et. al (2012). Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the stochastic block model (SBM), and its extensions, previous results on spectral clustering relied on the minimum degree of the graph being sufficiently large for its good performance. By examining the scenario where the regularization parameter $τ$ is large we show that the minimum degree assumption can potentially be removed. As a special case, for an SBM with two blocks, the results require the maximum degree to be large (grow faster than $\log n$) as opposed to the minimum degree. More importantly, we show the usefulness of regularization in situations where not all nodes belong to well-defined clusters. Our results rely on a `bias-variance'-like trade-off that arises from understanding the concentration of the sample Laplacian and the eigen gap as a function of the regularization parameter. As a byproduct of our bounds, we propose a data-driven technique \textit{DKest} (standing for estimated Davis-Kahan bounds) for choosing the regularization parameter. This technique is shown to work well through simulations and on a real data set.

Julien Mairal, Bin Yu

We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to automatically select a subgraph with few connected components; by exploiting prior knowledge, one can indeed improve the prediction performance or obtain results that are easier to interpret. Regularization or penalty functions for selecting features in graphs have recently been proposed, but they raise new algorithmic challenges. For example, they typically require solving a combinatorially hard selection problem among all connected subgraphs. In this paper, we propose computationally feasible strategies to select a sparse and well-connected subset of features sitting on a directed acyclic graph (DAG). We introduce structured sparsity penalties over paths on a DAG called "path coding" penalties. Unlike existing regularization functions that model long-range interactions between features in a graph, path coding penalties are tractable. The penalties and their proximal operators involve path selection problems, which we efficiently solve by leveraging network flow optimization. We experimentally show on synthetic, image, and genomic data that our approach is scalable and leads to more connected subgraphs than other regularization functions for graphs.

Karl Rohe, Tai Qin, Bin Yu

Directed graphs have asymmetric connections, yet the current graph clustering methodologies cannot identify the potentially global structure of these asymmetries. We give a spectral algorithm called di-sim that builds on a dual measure of similarity that correspond to how a node (i) sends and (ii) receives edges. Using di-sim, we analyze the global asymmetries in the networks of Enron emails, political blogs, and the c elegans neural connectome. In each example, a small subset of nodes have persistent asymmetries; these nodes send edges with one cluster, but receive edges with another cluster. Previous approaches would have assigned these asymmetric nodes to only one cluster, failing to identify their sending/receiving asymmetries. Regularization and "projection" are two steps of di-sim that are essential for spectral clustering algorithms to work in practice. The theoretical results show that these steps make the algorithm weakly consistent under the degree corrected Stochastic co-Blockmodel, a model that generalizes the Stochastic Blockmodel to allow for both (i) degree heterogeneity and (ii) the global asymmetries that we intend to detect. The theoretical results make no assumptions on the smallest degree nodes. Instead, the theorem requires that the average degree grows sufficiently fast and that the weak consistency only applies to the subset of the nodes with sufficiently large leverage scores. The results results also apply to bipartite graphs.