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Stephen Mussmann

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Machine Learning Computer Vision Data Structures and Algorithms

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preprint2026arXiv

Instance-Level Costs for Nuanced Classifier Evaluation

Standard classification treats all errors equally, but in content moderation, medical screening, and safety-critical applications, mistakes on clear-cut cases are far more costly than errors on ambiguous ones. We propose normalized excess cost (NEC), a metric that weights classification errors by per-example costs and reduces to standard error rate when costs are uniform. Costs can derive from annotator vote margins, distance from decision thresholds, or confidence ratings. Across text, image, and tabular benchmarks, we find that NEC is often substantially lower than error rate -- models with 5\% error rate can achieve 1.8\% NEC -- revealing that most mistakes concentrate on ambiguous, low-cost examples. However, incorporating costs into training via loss weighting, sampling strategies, or regression yields inconsistent benefits: improvements appear only when costs are predictable from input features, as in our synthetic control, while real-world datasets show mixed or negligible gains. Our framework provides a practical methodology for deriving and evaluating instance-level misclassification costs, even when cost-sensitive training offers limited benefit.

preprint2026arXiv

Sum Estimation via Vector Similarity Search

Semantic embeddings to represent objects such as image, text and audio are widely used in machine learning and have spurred the development of vector similarity search methods for retrieving semantically related objects. In this work, we study the sibling task of estimating a sum over all objects in a set, such as the kernel density estimate (KDE) and the normalizing constant for softmax distributions. While existing solutions provably reduce the sum estimation task to acquiring $\mathcal{O}(\sqrt{n})$ most similar vectors, where $n$ is the number of objects, we introduce a novel algorithm that only requires $\mathcal{O}(\log(n))$ most similar vectors. Our approach randomly assigns objects to levels with exponentially-decaying probabilities and constructs a vector similarity search data structure for each level. With the top-$k$ objects from each level, we propose an unbiased estimate of the sum and prove a high-probability relative error bound. We run experiments on OpenImages and Amazon Reviews with a vector similar search implementation to show that our method can achieve lower error using less computational time than existing reductions. We show results on applications in estimating densities, computing softmax denominators, and counting the number of vectors within a ball.

preprint2021arXiv

Comparing the Value of Labeled and Unlabeled Data in Method-of-Moments Latent Variable Estimation

Labeling data for modern machine learning is expensive and time-consuming. Latent variable models can be used to infer labels from weaker, easier-to-acquire sources operating on unlabeled data. Such models can also be trained using labeled data, presenting a key question: should a user invest in few labeled or many unlabeled points? We answer this via a framework centered on model misspecification in method-of-moments latent variable estimation. Our core result is a bias-variance decomposition of the generalization error, which shows that the unlabeled-only approach incurs additional bias under misspecification. We then introduce a correction that provably removes this bias in certain cases. We apply our decomposition framework to three scenarios -- well-specified, misspecified, and corrected models -- to 1) choose between labeled and unlabeled data and 2) learn from their combination. We observe theoretically and with synthetic experiments that for well-specified models, labeled points are worth a constant factor more than unlabeled points. With misspecification, however, their relative value is higher due to the additional bias but can be reduced with correction. We also apply our approach to study real-world weak supervision techniques for dataset construction.

preprint2020arXiv

Concept Bottleneck Models

We seek to learn models that we can interact with using high-level concepts: if the model did not think there was a bone spur in the x-ray, would it still predict severe arthritis? State-of-the-art models today do not typically support the manipulation of concepts like "the existence of bone spurs", as they are trained end-to-end to go directly from raw input (e.g., pixels) to output (e.g., arthritis severity). We revisit the classic idea of first predicting concepts that are provided at training time, and then using these concepts to predict the label. By construction, we can intervene on these concept bottleneck models by editing their predicted concept values and propagating these changes to the final prediction. On x-ray grading and bird identification, concept bottleneck models achieve competitive accuracy with standard end-to-end models, while enabling interpretation in terms of high-level clinical concepts ("bone spurs") or bird attributes ("wing color"). These models also allow for richer human-model interaction: accuracy improves significantly if we can correct model mistakes on concepts at test time.

preprint2015arXiv

Understanding Trajectory Behavior: A Motion Pattern Approach

Mining the underlying patterns in gigantic and complex data is of great importance to data analysts. In this paper, we propose a motion pattern approach to mine frequent behaviors in trajectory data. Motion patterns, defined by a set of highly similar flow vector groups in a spatial locality, have been shown to be very effective in extracting dominant motion behaviors in video sequences. Inspired by applications and properties of motion patterns, we have designed a framework that successfully solves the general task of trajectory clustering. Our proposed algorithm consists of four phases: flow vector computation, motion component extraction, motion component's reachability set creation, and motion pattern formation. For the first phase, we break down trajectories into flow vectors that indicate instantaneous movements. In the second phase, via a Kmeans clustering approach, we create motion components by clustering the flow vectors with respect to their location and velocity. Next, we create motion components' reachability set in terms of spatial proximity and motion similarity. Finally, for the fourth phase, we cluster motion components using agglomerative clustering with the weighted Jaccard distance between the motion components' signatures, a set created using path reachability. We have evaluated the effectiveness of our proposed method in an extensive set of experiments on diverse datasets. Further, we have shown how our proposed method handles difficulties in the general task of trajectory clustering that challenge the existing state-of-the-art methods.