Streaming Inference

We study streaming algorithms for the $\ell_p$ subspace approximation problem. Given points $a_1, \ldots, a_n$ as an insertion-only stream and a rank parameter $k$, the $\ell_p$ subspace approximation problem is to find a $k$-dimensional subspace $V$ such that $(\sum_{i=1}^n d(a_i, V)^p)^{1/p}$ is minimized, where $d(a, V)$ denotes the Euclidean distance between $a$ and $V$ defined as $\min_{v \in V} ||a - v||$. When $p = \infty$, we need to find a subspace $V$ that minimizes $\max_i d(a_i, V)$. For $\ell_{\infty}$ subspace approximation, we give a deterministic strong coreset construction algorithm and show that it can be used to compute a $\mathrm{poly}(k, \log n)$ approximate solution. We show that the distortion obtained by our coreset is nearly tight for any sublinear space algorithm. For $\ell_p$ subspace approximation, we show that suitably scaling the points and then using our $\ell_{\infty}$ coreset construction, we can compute a $\mathrm{poly}(k, \log n)$ approximation. Our algorithms are easy to implement and run very fast on large datasets. We also use our strong coreset construction to improve the results in a recent work of Woodruff and Yasuda (FOCS 2022) which gives streaming algorithms for high-dimensional geometric problems such as width estimation, convex hull estimation, and volume estimation.

Recently, the question of adversarially robust streaming, where the stream is allowed to depend on the randomness of the streaming algorithm, has gained a lot of attention. In this work, we consider a strong white-box adversarial model (Ajtai et al. PODS 2022), in which the adversary has access to all past random coins and the parameters used by the streaming algorithm. We focus on the sparse recovery problem and extend our result to other tasks such as distinct element estimation and low-rank approximation of matrices and tensors. The main drawback of previous work is that it requires a *random oracle*, which is especially problematic in the streaming model since the amount of randomness is counted in the space complexity of a streaming algorithm. Also, the previous work suffers from large update time. We construct a near-optimal solution for the sparse recovery problem in white-box adversarial streams, based on the subexponentially secure Learning with Errors assumption. Importantly, our solution does not require a random oracle and has a polylogarithmic per item processing time. We also give results in a related white-box adversarially robust distributed model. Our constructions are based on homomorphic encryption schemes satisfying very mild structural properties that are currently satisfied by most known schemes.

In digital markets comprised of many competing services, each user chooses between multiple service providers according to their preferences, and the chosen service makes use of the user data to incrementally improve its model. The service providers' models influence which service the user will choose at the next time step, and the user's choice, in return, influences the model update, leading to a feedback loop. In this paper, we formalize the above dynamics and develop a simple and efficient decentralized algorithm to locally minimize the overall user loss. Theoretically, we show that our algorithm asymptotically converges to stationary points of of the overall loss almost surely. We also experimentally demonstrate the utility of our algorithm with real world data.

Co-training is a classical semi-supervised learning method which only requires a small number of labeled examples for learning, under reasonable assumptions. Despite extensive literature on the topic, very few hypothesis classes are known to be provably efficiently learnable via co-training, even under very strong distributional assumptions. In this work, we study the co-training problem in the stream-based active learning model. We show that a range of natural concept classes are efficiently learnable via co-training, in terms of both label efficiency and computational efficiency. We provide an efficient reduction of co-training under the standard assumption of weak dependence, in the stream-based active model, to online classification. As a corollary, we obtain efficient co-training algorithms with error independent label complexity for every concept class class efficiently learnable in the mistake bound online model. Our framework also gives co-training algorithms with label complexity $\tilde{O}(d\log (1/\epsilon))$ for any concept class with VC dimension $d$, though in general this reduction is not computationally efficient. Finally, using additional ideas from online learning, we design the first efficient co-training algorithms with label complexity $\tilde{O}(d^2\log (1/\epsilon))$ for several concept classes, including unions of intervals and homogeneous halfspaces.

The anomaly detection literature is abundant with offline methods, which require repeated access to data in memory, and impose impractical assumptions when applied to a streaming context. Existing online anomaly detection methods also generally fail to address these constraints, resorting to periodic retraining to adapt to the online context. We propose Online-iForest, a novel method explicitly designed for streaming conditions that seamlessly tracks the data generating process as it evolves over time. Experimental validation on real-world datasets demonstrated that Online-iForest is on par with online alternatives and closely rivals state-of-the-art offline anomaly detection techniques that undergo periodic retraining. Notably, Online-iForest consistently outperforms all competitors in terms of efficiency, making it a promising solution in applications where fast identification of anomalies is of primary importance such as cybersecurity, fraud and fault detection.

Distributed LLM serving is costly and often underutilizes hardware accelerators due to three key challenges: bubbles in pipeline-parallel deployments caused by the bimodal latency of prompt and token processing, GPU memory overprovisioning, and long recovery times in case of failures. DéjàVu addresses all these challenges using a versatile and efficient KV cache streaming library (DéjàVuLib). Using DéjàVuLib, we propose and implement efficient prompt-token disaggregation to reduce pipeline bubbles, microbatch swapping for efficient GPU memory management, and state replication for fault-tolerance. We highlight the efficacy of these solutions on a range of large models across cloud deployments.