Michael Mitzenmacher

Eric R. Knorr, Baptiste Lemaire, Andrew Lim et al.

We introduce Proteus, a novel self-designing approximate range filter, which configures itself based on sampled data in order to optimize its false positive rate (FPR) for a given space requirement. Proteus unifies the probabilistic and deterministic design spaces of state-of-the-art range filters to achieve robust performance across a larger variety of use cases. At the core of Proteus lies our Contextual Prefix FPR (CPFPR) model - a formal framework for the FPR of prefix-based filters across their design spaces. We empirically demonstrate the accuracy of our model and Proteus' ability to optimize over both synthetic workloads and real-world datasets. We further evaluate Proteus in RocksDB and show that it is able to improve end-to-end performance by as much as 5.3x over more brittle state-of-the-art methods such as SuRF and Rosetta. Our experiments also indicate that the cost of modeling is not significant compared to the end-to-end performance gains and that Proteus is robust to workload shifts.

Minghao Li, Ran Ben Basat, Shay Vargaftik et al.

Deep neural networks (DNNs) are the de facto standard for essential use cases, such as image classification, computer vision, and natural language processing. As DNNs and datasets get larger, they require distributed training on increasingly larger clusters. A main bottleneck is the resulting communication overhead where workers exchange model updates (i.e., gradients) on a per-round basis. To address this bottleneck and accelerate training, a widely-deployed approach is compression. However, previous deployments often apply bi-directional compression schemes by simply using a uni-directional gradient compression scheme in each direction. This results in significant computational overheads at the parameter server and increased compression error, leading to longer training and lower accuracy. We introduce Tensor Homomorphic Compression (THC), a novel bi-directional compression framework that enables the direct aggregation of compressed values and thus eliminating the aforementioned computational overheads. Moreover, THC is compatible with in-network aggregation (INA), which allows for further acceleration. Our evaluation shows that training representative vision and language models with THC reaches target accuracy by 1.40x to 1.47x faster using INA and 1.28x to 1.33x faster using a software PS compared with state-of-the-art systems.

Ran Ben Basat, Shay Vargaftik, Amit Portnoy et al.

Distributed Mean Estimation (DME), in which $n$ clients communicate vectors to a parameter server that estimates their average, is a fundamental building block in communication-efficient federated learning. In this paper, we improve on previous DME techniques that achieve the optimal $O(1/n)$ Normalized Mean Squared Error (NMSE) guarantee by asymptotically improving the complexity for either encoding or decoding (or both). To achieve this, we formalize the problem in a novel way that allows us to use off-the-shelf mathematical solvers to design the quantization.

Maximilian Lam, Michael Mitzenmacher, Vijay Janapa Reddi et al.

Multiparty computation approaches to secure neural network inference commonly rely on garbled circuits for securely executing nonlinear activation functions. However, garbled circuits require excessive communication between server and client, impose significant storage overheads, and incur large runtime penalties. To reduce these costs, we propose an alternative to garbled circuits: Tabula, an algorithm based on secure lookup tables. Our approach precomputes lookup tables during an offline phase that contains the result of all possible nonlinear function calls. Because these tables incur exponential storage costs in the number of operands and the precision of the input values, we use quantization to reduce these storage costs to make this approach practical. This enables an online phase where securely computing the result of a nonlinear function requires just a single round of communication, with communication cost equal to twice the number of bits of the input to the nonlinear function. In practice our approach costs 2 bytes of communication per nonlinear function call in the online phase. Compared to garbled circuits with 8-bit quantized inputs, when computing individual nonlinear functions during the online phase, experiments show Tabula with 8-bit activations uses between $280$-$560 \times$ less communication, is over $100\times$ faster, and uses a comparable (within a factor of 2) amount of storage; compared against other state-of-the-art protocols Tabula achieves greater than $40\times$ communication reduction. This leads to significant performance gains over garbled circuits with quantized inputs during the online phase of secure inference of neural networks: Tabula reduces end-to-end inference communication by up to $9 \times$ and achieves an end-to-end inference speedup of up to $50 \times$, while imposing comparable storage and offline preprocessing costs.

Ran Ben-Basat, Yaniv Ben-Itzhak, Gal Mendelson et al.

This note clarifies the relationship between the recent TurboQuant work and the earlier DRIVE (NeurIPS 2021) and EDEN (ICML 2022) schemes. DRIVE is a 1-bit quantizer that EDEN extended to any $b>0$ bits per coordinate; we refer to them collectively as EDEN. First, TurboQuant$_{\text{mse}}$ is a special case of EDEN obtained by fixing EDEN's scalar scale parameter to $S=1$. EDEN supports both biased and unbiased quantization, each optimized by a different $S$ (chosen via methods described in the EDEN works). The fixed choice $S=1$ used by TurboQuant is generally suboptimal, although the optimal $S$ for biased EDEN converges to $1$ as the dimension grows; accordingly TurboQuant$_{\text{mse}}$ approaches EDEN's behavior for large $d$. Second, TurboQuant$_{\text{prod}}$ combines a biased $(b-1)$-bit EDEN step with an unbiased 1-bit QJL quantization of the residual. It is suboptimal in three ways: (1) its $(b-1)$-bit step uses the suboptimal $S=1$; (2) its 1-bit unbiased residual quantization has worse MSE than (unbiased) 1-bit EDEN; (3) chaining a biased $(b-1)$-bit step with a 1-bit unbiased residual step is inferior to unbiasedly quantizing the input directly with $b$-bit EDEN. Third, some of the analysis in the TurboQuant work mirrors that of the EDEN works: both exploit the connection between random rotations and the shifted Beta distribution, use the Lloyd-Max algorithm, and note that Randomized Hadamard Transforms can replace uniform random rotations. Experiments support these claims: biased EDEN (with optimized $S$) is more accurate than TurboQuant$_{\text{mse}}$, and unbiased EDEN is markedly more accurate than TurboQuant$_{\text{prod}}$, often by more than a bit (e.g., 2-bit EDEN beats 3-bit TurboQuant$_{\text{prod}}$). We also repeat all accuracy experiments from the TurboQuant paper, showing that EDEN outperforms it in every setup we have tried.

Wenchen Han, Shay Vargaftik, Michael Mitzenmacher et al.

Gradient aggregation has long been identified as a major bottleneck in today's large-scale distributed machine learning training systems. One promising solution to mitigate such bottlenecks is gradient compression, directly reducing communicated gradient data volume. However, in practice, many gradient compression schemes do not achieve acceleration of the training process while also preserving accuracy. In this work, we identify common issues in previous gradient compression systems and evaluation methodologies. These include excessive computational overheads; incompatibility with all-reduce; and insufficient evaluation methods, such as not using an end-to-end metric or using a 32-bit baseline instead of the stronger 16-bit baseline. We revisit common compression approaches (sparsification, quantization, and low-rank decomposition) and demonstrate how considering the above issues can lead to minor but strategic design changes, resulting in notably better performance. Our goal is to raise awareness of the need for design and evaluation standards that naturally translate to the end-to-end utility of gradient compression.

Weifan Jiang, Rana Shahout, Minghao Li et al.

Multi-Agent Debate (MAD) improves LLM-agent accuracy but suffers from rapid context growth, limiting scalability in larger multi-agent settings. Existing methods prune low-utility communications using prior signals, such as token-level log-likelihoods or LLM self-reported confidence. However, these signals become unreliable under hallucination, degrading the accuracy of MAD methods that rely on them. We propose SVR-MAD, a Bayesian-inspired MAD framework that treats pre-debate signals as priors and debate outcomes as posterior-style evidence for estimating agent correctness. SVR-MAD uses this evidence to incrementally construct the communication graph, prioritizing agents whose answers survive peer challenges. Experiments across multiple LLMs and benchmarks show that SVR-MAD reduces token cost by up to 61% while matching or improving accuracy relative to the most accurate competing MAD baseline.

Wenchen Han, Shay Vargaftik, Michael Mitzenmacher et al.

Multi-hop all-reduce is the de facto backbone of large model training. As the training scale increases, the network often becomes a bottleneck, motivating reducing the volume of transmitted data. Accordingly, recent systems demonstrated significant acceleration of the training process using gradient quantization. However, these systems are not optimized for multi-hop aggregation, where entries are partially summed multiple times along their aggregation topology. This paper presents DynamiQ, a quantization framework that bridges the gap between quantization best practices and multi-hop aggregation. DynamiQ introduces novel techniques to better represent partial sums, co-designed with a decompress-accumulate-recompress fused kernel to facilitate fast execution. We extended PyTorch DDP to support DynamiQ over NCCL P2P, and across different LLMs, tasks, and scales, we demonstrate consistent improvement of up to 34.2% over the best among state-of-the-art methods such as Omni-Reduce, THC, and emerging standards such as MXFP4, MXFP6, and MXFP8. Further, DynamiQ is the only evaluated method that consistently reaches near-baseline accuracy (e.g., 99.9% of the BF16 baseline) and does so while significantly accelerating the training.

Rana Shahout, Ibrahim Sabek, Michael Mitzenmacher

We show how to utilize machine learning approaches to improve sliding window algorithms for approximate frequency estimation problems, under the ``algorithms with predictions'' framework. In this dynamic environment, previous learning-augmented algorithms are less effective, since properties in sliding window resolution can differ significantly from the properties of the entire stream. Our focus is on the benefits of predicting and filtering out items with large next arrival times -- that is, there is a large gap until their next appearance -- from the stream, which we show improves the memory-accuracy tradeoffs significantly. We provide theorems that provide insight into how and by how much our technique can improve the sliding window algorithm, as well as experimental results using real-world data sets. Our work demonstrates that predictors can be useful in the challenging sliding window setting.

Rana Shahout, Hayder Tirmazi, Minlan Yu et al.

We introduce Orla, a library for constructing and running LLM-based agentic systems. Modern agentic applications consist of workflows that combine multiple LLM inference steps, tool calls, and heterogeneous infrastructure. Today, developers typically build these systems by manually composing orchestration code with LLM serving engines and tool execution logic. Orla provides a general abstraction that separates request execution from workflow-level policy. It acts as a serving layer above existing LLM inference engines: developers define workflows composed of stages, while Orla manages how those stages are mapped, executed, and coordinated across models and backends. It provides agent-level control through three mechanisms: a stage mapper, which assigns each stage to an appropriate model and backend; a workflow orchestrator, which schedules stages and manages their resources and context; and a memory manager, which manages inference state such as the KV cache across workflow boundaries. We demonstrate Orla with a customer support workflow that exercises many of its capabilities. We evaluate Orla on two datasets, showing that stage mapping improves latency and cost compared to a single-model vLLM baseline, while workflow-level cache management reduces time-to-first-token.

Ran Ben-Basat, William Kuszmaul, Michael Mitzenmacher et al.

Uniform random rotations (URRs) are a common preprocessing step in modern quantization approaches used for gradient compression, inference acceleration, KV-cache compression, model weight quantization, and approximate nearest-neighbor search in vector databases. In practice, URRs are often replaced by randomized Hadamard transforms (RHTs), which preserve orthogonality while admitting fast implementations. The remaining issue is the performance for worst-case inputs. With a URR, each coordinate is individually distributed as a shifted beta distribution, which converges to a Gaussian distribution in high dimensions. Generally, one RHT is not suitable in the worst case, as individual coordinates can be far from these distributions. We show that after composing two RHTs on any $d$-sized input vector, the marginal distribution of every fixed coordinate of the normalized rotated vector is within $O(d^{-1/2})$ of a standard Gaussian both in Kolmogorov distance and in $1$-Wasserstein distance. We then plug these bounds into the analyses of modern compression schemes, namely DRIVE and QUIC-FL, and show that two RHTs achieve performance that asymptotically matches URRs. However, we show that two RHTs may not be sufficient for Vector Quantization (VQ), which often requires weak correlation across fixed-size blocks of coordinates (as opposed to only marginal distribution convergence for single coordinates). We prove that a composition of three RHTs leads to decaying coordinate covariance. This ensures that any fixed, bounded, multi-dimensional VQ codebook optimized for URRs has the same expected error when using three RHTs, up to an additive term that vanishes with the dimension. Finally, because practical inputs are rarely adversarial, we propose a linear-time ${O}(d)$ check on the input's moments to dynamically adapt the number of RHTs used at runtime to improve performance.

Rana Shahout, Cong Liang, Shiji Xin et al.

Augmented Large Language Models (LLMs) enhance the capabilities of standalone LLMs by integrating external data sources through API calls. In interactive LLM applications, efficient scheduling is crucial for maintaining low request completion times, directly impacting user engagement. However, these augmentations introduce scheduling challenges due to the need to manage limited memory for cached information (KV caches). As a result, traditional size-based scheduling algorithms, such as Shortest Job First (SJF), become less effective at minimizing completion times. Existing work focuses only on handling requests during API calls by preserving, discarding, or swapping memory without considering how to schedule requests with API calls. In this paper, we propose LAMPS, a novel LLM inference framework for augmented LLMs. LAMPS minimizes request completion time through a unified scheduling approach that considers the total length of requests and their handling strategies during API calls. Recognizing that LLM inference is memory-bound, our approach ranks requests based on their consumption of memory over time, which depends on both the output sizes and how a request is managed during its API calls. To implement our scheduling, LAMPS predicts the strategy that minimizes memory waste of a request during its API calls, aligning with but improving upon existing approaches. We also propose starvation prevention techniques and optimizations to mitigate the overhead of our scheduling. We implement LAMPS on top of vLLM and evaluate its performance against baseline LLM inference systems, demonstrating improvements in end-to-end latency by 27%-85% and reductions in TTFT by 4%-96% compared to the existing augmented-LLM system, with even greater gains over vLLM.

Michael Mitzenmacher, Rana Shahout

Queueing systems present many opportunities for applying machine-learning predictions, such as estimated service times, to improve system performance. This integration raises numerous open questions about how predictions can be effectively leveraged to improve scheduling decisions. Recent studies explore queues with predicted service times, typically aiming to minimize job time in the system. We review these works, highlight the effectiveness of predictions, and present open questions on queue performance. We then move to consider an important practical example of using predictions in scheduling, namely Large Language Model (LLM) systems, which presents novel scheduling challenges and highlights the potential for predictions to improve performance. In particular, we consider LLMs performing inference. Inference requests (jobs) in LLM systems are inherently complex; they have variable inference times, dynamic memory footprints that are constrained by key-value (KV) store memory limitations, and multiple possible preemption approaches that affect performance differently. We provide background on the important aspects of scheduling in LLM systems, and introduce new models and open problems that arise from them. We argue that there are significant opportunities for applying insights and analysis from queueing theory to scheduling in LLM systems.

Rana Shahout, Michael Mitzenmacher

In light of recent work on scheduling with predicted job sizes, we consider the effect of the cost of predictions in queueing systems, removing the assumption in prior research that predictions are external to the system's resources and/or cost-free. In particular, we introduce a novel approach to utilizing predictions, SkipPredict, designed to address their inherent cost. Rather than uniformly applying predictions to all jobs, we propose a tailored approach that categorizes jobs based on their prediction requirements. To achieve this, we employ one-bit "cheap predictions" to classify jobs as either short or long. SkipPredict prioritizes predicted short jobs over long jobs, and for the latter, SkipPredict applies a second round of more detailed "expensive predictions" to approximate Shortest Remaining Processing Time for these jobs. Our analysis takes into account the cost of prediction. We examine the effect of this cost for two distinct models. In the external cost model, predictions are generated by some external method without impacting job service times but incur a cost. In the server time cost model, predictions themselves require server processing time, and are scheduled on the same server as the jobs.

Ran Ben-Basat, Yaniv Ben-Itzhak, Michael Mitzenmacher et al.

Quantization is a fundamental optimization for many machine-learning use cases, including compressing gradients, model weights and activations, and datasets. The most accurate form of quantization is \emph{adaptive}, where the error is minimized with respect to a given input, rather than optimizing for the worst case. However, optimal adaptive quantization methods are considered infeasible in terms of both their runtime and memory requirements. We revisit the Adaptive Vector Quantization (AVQ) problem and present algorithms that find optimal solutions with asymptotically improved time and space complexity. We also present an even faster near-optimal algorithm for large inputs. Our experiments show our algorithms may open the door to using AVQ more extensively in a variety of machine learning applications.

Rana Shahout, Colin Cai, Yilun Du et al.

Mixture-of-Experts (MoE) models can scale parameter capacity by routing each token to a subset of experts through a learned gate function. While conditional routing reduces training costs, it shifts the burden on inference memory: expert parameters and activations consume memory, limiting the number of experts per device. As tokens are routed, some experts become overloaded while others are underutilized. Because experts are mapped to GPUs, this imbalance translates directly into degraded system performance in terms of latency, throughput, and cost. We present LASER, a plug-and-play, inference-time routing algorithm that balances load while preserving accuracy. LASER adapts to the shape of the gate's score distribution. When scores provide a clear preference, it routes to the strongest experts; when scores are more uniform, it broadens the set of viable experts and routes to the least-loaded among them. Because LASER relies only on gate scores from a trained model, it integrates directly into existing MoE inference pipelines without retraining or finetuning. We evaluate LASER on Mixtral-8x7B and DeepSeek-MoE-16b-chat across four datasets (ARC-Easy, ARC-Challenge, MMLU, and GSM8K). LASER improves load balancing, translating into lower latency and higher throughput, while keeping the accuracy changes negligible.

Weifan Jiang, Rana Shahout, Yilun Du et al.

Large Language Models (LLMs) increasingly rely on inference-time reasoning algorithms such as chain-of-thought and multi-branch reasoning to improve accuracy on complex tasks. These methods, however, substantially increase token usage and per-request latency. Prior work has largely focused on reducing token usage, often at the expense of accuracy, while overlooking other latency factors. We present DUCHESS, an LLM serving system that reduces cost and latency without sacrificing accuracy through intra-request branch orchestration guided by predictions. DUCHESS employs a lightweight linear probing model over LLM layer activations to estimate branch correctness, and its orchestration policy decides whether to terminate, duplicate, or continue a branch. When handling multiple requests, DUCHESS further reduces latency by prioritizing easier reasoning tasks when complexity can be estimated from the prompt. Experiments on three reasoning benchmarks show that DUCHESS consistently improves the token-accuracy Pareto frontier, reducing token usage by 42-63% at matched accuracy compared to self-consistency. In serving with vLLM, DUCHESS reduces mean, median, and tail latencies by 57-81%, 58-85%, and 52-84% with First-Come-First-Served scheduling, and achieves additional gains under difficulty-aware scheduling at higher request rates.

Zeyu Zhang, Haiying Shen, Shay Vargaftik et al.

Disaggregated Large Language Model (LLM) inference has gained popularity as it separates the computation-intensive prefill stage from the memory-intensive decode stage, avoiding the prefill-decode interference and improving resource utilization. However, transmitting Key-Value (KV) data between the two stages can be a bottleneck, especially for long prompts. Additionally, the computation time overhead for prefill and decode is key for optimizing Job Completion Time (JCT), and KV data size can become prohibitive for long prompts and sequences. Existing KV quantization methods can alleviate the transmission bottleneck and reduce memory requirements, but they introduce significant dequantization overhead, exacerbating the computation time. We propose Homomorphic Acceleration via Compression of the KV cache (HACK) for disaggregated LLM inference. HACK eliminates the heavy KV dequantization step, and directly performs computations on quantized KV data to approximate and reduce the cost of the expensive matrix-multiplication step. Extensive trace-driven experiments show that HACK reduces JCT by up to 70.9% compared to disaggregated LLM inference baseline and by up to 52.3% compared to state-of-the-art KV quantization methods.

Rana Shahout, Michael Mitzenmacher

Identifying heavy hitters and estimating the frequencies of flows are fundamental tasks in various network domains. Existing approaches to this challenge can broadly be categorized into two groups, hashing-based and competing-counter-based. The Count-Min sketch is a standard example of a hashing-based algorithm, and the Space Saving algorithm is an example of a competing-counter algorithm. Recent works have explored the use of machine learning to enhance algorithms for frequency estimation problems, under the algorithms with prediction framework. However, these works have focused solely on the hashing-based approach, which may not be best for identifying heavy hitters. In this paper, we present the first learned competing-counter-based algorithm, called LSS, for identifying heavy hitters, top k, and flow frequency estimation that utilizes the well-known Space Saving algorithm. We provide theoretical insights into how and to what extent our approach can improve upon Space Saving, backed by experimental results on both synthetic and real-world datasets. Our evaluation demonstrates that LSS can enhance the accuracy and efficiency of Space Saving in identifying heavy hitters, top k, and estimating flow frequencies.

Shay Vargaftik, Ran Ben Basat, Amit Portnoy et al.

Distributed Mean Estimation (DME) is a central building block in federated learning, where clients send local gradients to a parameter server for averaging and updating the model. Due to communication constraints, clients often use lossy compression techniques to compress the gradients, resulting in estimation inaccuracies. DME is more challenging when clients have diverse network conditions, such as constrained communication budgets and packet losses. In such settings, DME techniques often incur a significant increase in the estimation error leading to degraded learning performance. In this work, we propose a robust DME technique named EDEN that naturally handles heterogeneous communication budgets and packet losses. We derive appealing theoretical guarantees for EDEN and evaluate it empirically. Our results demonstrate that EDEN consistently improves over state-of-the-art DME techniques.

Maximilian Lam, Gu-Yeon Wei, David Brooks et al.

We show that aggregated model updates in federated learning may be insecure. An untrusted central server may disaggregate user updates from sums of updates across participants given repeated observations, enabling the server to recover privileged information about individual users' private training data via traditional gradient inference attacks. Our method revolves around reconstructing participant information (e.g: which rounds of training users participated in) from aggregated model updates by leveraging summary information from device analytics commonly used to monitor, debug, and manage federated learning systems. Our attack is parallelizable and we successfully disaggregate user updates on settings with up to thousands of participants. We quantitatively and qualitatively demonstrate significant improvements in the capability of various inference attacks on the disaggregated updates. Our attack enables the attribution of learned properties to individual users, violating anonymity, and shows that a determined central server may undermine the secure aggregation protocol to break individual users' data privacy in federated learning.

Shay Vargaftik, Ran Ben Basat, Amit Portnoy et al.

We consider the problem where $n$ clients transmit $d$-dimensional real-valued vectors using $d(1+o(1))$ bits each, in a manner that allows the receiver to approximately reconstruct their mean. Such compression problems naturally arise in distributed and federated learning. We provide novel mathematical results and derive computationally efficient algorithms that are more accurate than previous compression techniques. We evaluate our methods on a collection of distributed and federated learning tasks, using a variety of datasets, and show a consistent improvement over the state of the art.

Ran Ben-Basat, Michael Mitzenmacher, Shay Vargaftik

We consider the fundamental problem of communicating an estimate of a real number $x\in[0,1]$ using a single bit. A sender that knows $x$ chooses a value $X\in\set{0,1}$ to transmit. In turn, a receiver estimates $x$ based on the value of $X$. We consider both the biased and unbiased estimation problems and aim to minimize the cost. For the biased case, the cost is the worst-case (over the choice of $x$) expected squared error, which coincides with the variance if the algorithm is required to be unbiased. We first overview common biased and unbiased estimation approaches and prove their optimality when no shared randomness is allowed. We then show how a small amount of shared randomness, which can be as low as a single bit, reduces the cost in both cases. Specifically, we derive lower bounds on the cost attainable by any algorithm with unrestricted use of shared randomness and propose near-optimal solutions that use a small number of shared random bits. Finally, we discuss open problems and future directions.

Michael Mitzenmacher

Motivated by recent work on scheduling with predicted job sizes, we consider the performance of scheduling algorithms with minimal advice, namely a single bit. Besides demonstrating the power of very limited advice, such schemes are quite natural. In the prediction setting, one bit of advice can be used to model a simple prediction as to whether a job is "large" or "small"; that is, whether a job is above or below a given threshold. Further, one-bit advice schemes can correspond to mechanisms that tell whether to put a job at the front or the back for the queue, a limitation which may be useful in many implementation settings. Finally, queues with a single bit of advice have a simple enough state that they can be analyzed in the limiting mean-field analysis framework for the power of two choices. Our work follows in the path of recent work by showing that even small amounts of even possibly inaccurate information can greatly improve scheduling performance.

Kapil Vaidya, Eric Knorr, Tim Kraska et al.

Bloom filters are space-efficient probabilistic data structures that are used to test whether an element is a member of a set, and may return false positives. Recently, variations referred to as learned Bloom filters were developed that can provide improved performance in terms of the rate of false positives, by using a learned model for the represented set. However, previous methods for learned Bloom filters do not take full advantage of the learned model. Here we show how to frame the problem of optimal model utilization as an optimization problem, and using our framework derive algorithms that can achieve near-optimal performance in many cases. Experimental results from both simulated and real-world datasets show significant performance improvements from our optimization approach over both the original learned Bloom filter constructions and previously proposed heuristic improvements.

Kasper Green Larsen, Michael Mitzenmacher, Charalampos E. Tsourakakis

We consider the following problem, which is useful in applications such as joint image and shape alignment. The goal is to recover $n$ discrete variables $g_i \in \{0, \ldots, k-1\}$ (up to some global offset) given noisy observations of a set of their pairwise differences $\{(g_i - g_j) \bmod k\}$; specifically, with probability $\frac{1}{k}+δ$ for some $δ> 0$ one obtains the correct answer, and with the remaining probability one obtains a uniformly random incorrect answer. We consider a learning-based formulation where one can perform a query to observe a pairwise difference, and the goal is to perform as few queries as possible while obtaining the exact joint alignment. We provide an easy-to-implement, time efficient algorithm that performs $O\big(\frac{n \lg n}{k δ^2}\big)$ queries, and recovers the joint alignment with high probability. We also show that our algorithm is optimal by proving a general lower bound that holds for all non-adaptive algorithms. Our work improves significantly recent work by Chen and Candés \cite{chen2016projected}, who view the problem as a constrained principal components analysis problem that can be solved using the power method. Specifically, our approach is simpler both in the algorithm and the analysis, and provides additional insights into the problem structure.

Michael Mitzenmacher, Matteo Dell'Amico

The supermarket model refers to a system with a large number of queues, where new customers choose d queues at random and join the one with the fewest customers. This model demonstrates the power of even small amounts of choice, as compared to simply joining a queue chosen uniformly at random, for load balancing systems. In this work we perform simulation-based studies to consider variations where service times for a customer are predicted, as might be done in modern settings using machine learning techniques or related mechanisms. Our primary takeaway is that using even seemingly weak predictions of service times can yield significant benefits over blind First In First Out queueing in this context. However, some care must be taken when using predicted service time information to both choose a queue and order elements for service within a queue; while in many cases using the information for both choosing and ordering is beneficial, in many of our simulation settings we find that simply using the number of jobs to choose a queue is better when using predicted service times to order jobs in a queue. In our simulations, we evaluate both synthetic and real-world workloads--in the latter, service times are predicted by machine learning. Our results provide practical guidance for the design of real-world systems; moreover, we leave many natural theoretical open questions for future work, validating their relevance to real-world situations.

Hossein Esfandiari, MohammadTaghi Hajiaghayi, Brendan Lucier et al.

We consider online variations of the Pandora's box problem (Weitzman. 1979), a standard model for understanding issues related to the cost of acquiring information for decision-making. Our problem generalizes both the classic Pandora's box problem and the prophet inequality framework. Boxes are presented online, each with a random value and cost drew jointly from some known distribution. Pandora chooses online whether to open each box given its cost, and then chooses irrevocably whether to keep the revealed prize or pass on it. We aim for approximation algorithms against adversaries that can choose the largest prize over any opened box, and use optimal offline policies to decide which boxes to open (without knowledge of the value inside). We consider variations where Pandora can collect multiple prizes subject to feasibility constraints, such as cardinality, matroid, or knapsack constraints. We also consider variations related to classic multi-armed bandit problems from reinforcement learning. Our results use a reduction-based framework where we separate the issues of the cost of acquiring information from the online decision process of which prizes to keep. Our work shows that in many scenarios, Pandora can achieve a good approximation to the best possible performance.

Michael Mitzenmacher

Recent work has suggested enhancing Bloom filters by using a pre-filter, based on applying machine learning to determine a function that models the data set the Bloom filter is meant to represent. Here we model such learned Bloom filters,, with the following outcomes: (1) we clarify what guarantees can and cannot be associated with such a structure; (2) we show how to estimate what size the learning function must obtain in order to obtain improved performance; (3) we provide a simple method, sandwiching, for optimizing learned Bloom filters; and (4) we propose a design and analysis approach for a learned Bloomier filter, based on our modeling approach.

Charalampos E. Tsourakakis, Michael Mitzenmacher, Kasper Green Larsen et al.

Social networks involve both positive and negative relationships, which can be captured in signed graphs. The {\em edge sign prediction problem} aims to predict whether an interaction between a pair of nodes will be positive or negative. We provide theoretical results for this problem that motivate natural improvements to recent heuristics. The edge sign prediction problem is related to correlation clustering; a positive relationship means being in the same cluster. We consider the following model for two clusters: we are allowed to query any pair of nodes whether they belong to the same cluster or not, but the answer to the query is corrupted with some probability $0<q<\frac{1}{2}$. Let $δ=1-2q$ be the bias. We provide an algorithm that recovers all signs correctly with high probability in the presence of noise with $O(\frac{n\log n}{δ^2}+\frac{\log^2 n}{δ^6})$ queries. This is the best known result for this problem for all but tiny $δ$, improving on the recent work of Mazumdar and Saha \cite{mazumdar2017clustering}. We also provide an algorithm that performs $O(\frac{n\log n}{δ^4})$ queries, and uses breadth first search as its main algorithmic primitive. While both the running time and the number of queries for this algorithm are sub-optimal, our result relies on novel theoretical techniques, and naturally suggests the use of edge-disjoint paths as a feature for predicting signs in online social networks. Correspondingly, we experiment with using edge disjoint $s-t$ paths of short length as a feature for predicting the sign of edge $(s,t)$ in real-world signed networks. Empirical findings suggest that the use of such paths improves the classification accuracy, especially for pairs of nodes with no common neighbors.

Max Hopkins, Michael Mitzenmacher, Sebastian Wagner-Carena

JPEG is one of the most widely used image formats, but in some ways remains surprisingly unoptimized, perhaps because some natural optimizations would go outside the standard that defines JPEG. We show how to improve JPEG compression in a standard-compliant, backward-compatible manner, by finding improved default quantization tables. We describe a simulated annealing technique that has allowed us to find several quantization tables that perform better than the industry standard, in terms of both compressed size and image fidelity. Specifically, we derive tables that reduce the FSIM error by over 10% while improving compression by over 20% at quality level 95 in our tests; we also provide similar results for other quality levels. While we acknowledge our approach can in some images lead to visible artifacts under large magnification, we believe use of these quantization tables, or additional tables that could be found using our methodology, would significantly reduce JPEG file sizes with improved overall image quality.

David Eppstein, Michael T. Goodrich, Jenny Lam et al.

We introduce models and algorithmic foundations for graph watermarking. Our frameworks include security definitions and proofs, as well as characterizations when graph watermarking is algorithmically feasible, in spite of the fact that the general problem is NP-complete by simple reductions from the subgraph isomorphism or graph edit distance problems. In the digital watermarking of many types of files, an implicit step in the recovery of a watermark is the mapping of individual pieces of data, such as image pixels or movie frames, from one object to another. In graphs, this step corresponds to approximately matching vertices of one graph to another based on graph invariants such as vertex degree. Our approach is based on characterizing the feasibility of graph watermarking in terms of keygen, marking, and identification functions defined over graph families with known distributions. We demonstrate the strength of this approach with exemplary watermarking schemes for two random graph models, the classic Erdős-Rényi model and a random power-law graph model, both of which are used to model real-world networks.

Ping Li, Michael Mitzenmacher, Anshumali Shrivastava

The method of random projections has become a standard tool for machine learning, data mining, and search with massive data at Web scale. The effective use of random projections requires efficient coding schemes for quantizing (real-valued) projected data into integers. In this paper, we focus on a simple 2-bit coding scheme. In particular, we develop accurate nonlinear estimators of data similarity based on the 2-bit strategy. This work will have important practical applications. For example, in the task of near neighbor search, a crucial step (often called re-ranking) is to compute or estimate data similarities once a set of candidate data points have been identified by hash table techniques. This re-ranking step can take advantage of the proposed coding scheme and estimator. As a related task, in this paper, we also study a simple uniform quantization scheme for the purpose of building hash tables with projected data. Our analysis shows that typically only a small number of bits are needed. For example, when the target similarity level is high, 2 or 3 bits might be sufficient. When the target similarity level is not so high, it is preferable to use only 1 or 2 bits. Therefore, a 2-bit scheme appears to be overall a good choice for the task of sublinear time approximate near neighbor search via hash tables. Combining these results, we conclude that 2-bit random projections should be recommended for approximate near neighbor search and similarity estimation. Extensive experimental results are provided.

Yakir A. Reshef, David N. Reshef, Pardis C. Sabeti et al.

The maximal information coefficient (MIC) is a tool for finding the strongest pairwise relationships in a data set with many variables (Reshef et al., 2011). MIC is useful because it gives similar scores to equally noisy relationships of different types. This property, called {\em equitability}, is important for analyzing high-dimensional data sets. Here we formalize the theory behind both equitability and MIC in the language of estimation theory. This formalization has a number of advantages. First, it allows us to show that equitability is a generalization of power against statistical independence. Second, it allows us to compute and discuss the population value of MIC, which we call MIC_*. In doing so we generalize and strengthen the mathematical results proven in Reshef et al. (2011) and clarify the relationship between MIC and mutual information. Introducing MIC_* also enables us to reason about the properties of MIC more abstractly: for instance, we show that MIC_* is continuous and that there is a sense in which it is a canonical "smoothing" of mutual information. We also prove an alternate, equivalent characterization of MIC_* that we use to state new estimators of it as well as an algorithm for explicitly computing it when the joint probability density function of a pair of random variables is known. Our hope is that this paper provides a richer theoretical foundation for MIC and equitability going forward. This paper will be accompanied by a forthcoming companion paper that performs extensive empirical analysis and comparison to other methods and discusses the practical aspects of both equitability and the use of MIC and its related statistics.

Ping Li, Michael Mitzenmacher, Anshumali Shrivastava

This technical note compares two coding (quantization) schemes for random projections in the context of sub-linear time approximate near neighbor search. The first scheme is based on uniform quantization while the second scheme utilizes a uniform quantization plus a uniformly random offset (which has been popular in practice). The prior work compared the two schemes in the context of similarity estimation and training linear classifiers, with the conclusion that the step of random offset is not necessary and may hurt the performance (depending on the similarity level). The task of near neighbor search is related to similarity estimation with importance distinctions and requires own study. In this paper, we demonstrate that in the context of near neighbor search, the step of random offset is not needed either and may hurt the performance (sometimes significantly so, depending on the similarity and other parameters).

Ping Li, Michael Mitzenmacher, Anshumali Shrivastava

The method of random projections has become very popular for large-scale applications in statistical learning, information retrieval, bio-informatics and other applications. Using a well-designed coding scheme for the projected data, which determines the number of bits needed for each projected value and how to allocate these bits, can significantly improve the effectiveness of the algorithm, in storage cost as well as computational speed. In this paper, we study a number of simple coding schemes, focusing on the task of similarity estimation and on an application to training linear classifiers. We demonstrate that uniform quantization outperforms the standard existing influential method (Datar et. al. 2004). Indeed, we argue that in many cases coding with just a small number of bits suffices. Furthermore, we also develop a non-uniform 2-bit coding scheme that generally performs well in practice, as confirmed by our experiments on training linear support vector machines (SVM).

David Reshef, Yakir Reshef, Michael Mitzenmacher et al.

A measure of dependence is said to be equitable if it gives similar scores to equally noisy relationships of different types. Equitability is important in data exploration when the goal is to identify a relatively small set of strongest associations within a dataset as opposed to finding as many non-zero associations as possible, which often are too many to sift through. Thus an equitable statistic, such as the maximal information coefficient (MIC), can be useful for analyzing high-dimensional data sets. Here, we explore both equitability and the properties of MIC, and discuss several aspects of the theory and practice of MIC. We begin by presenting an intuition behind the equitability of MIC through the exploration of the maximization and normalization steps in its definition. We then examine the speed and optimality of the approximation algorithm used to compute MIC, and suggest some directions for improving both. Finally, we demonstrate in a range of noise models and sample sizes that MIC is more equitable than natural alternatives, such as mutual information estimation and distance correlation.

Michael T. Goodrich, Michael Mitzenmacher

We study the question of how to shuffle $n$ cards when faced with an opponent who knows the initial position of all the cards {\em and} can track every card when permuted, {\em except} when one takes $K< n$ cards at a time and shuffles them in a private buffer "behind your back," which we call {\em buffer shuffling}. The problem arises naturally in the context of parallel mixnet servers as well as other security applications. Our analysis is based on related analyses of load-balancing processes. We include extensions to variations that involve corrupted servers and adversarially injected messages, which correspond to an opponent who can peek at some shuffles in the buffer and who can mark some number of the cards. In addition, our analysis makes novel use of a sum-of-squares metric for anonymity, which leads to improved performance bounds for parallel mixnets and can also be used to bound well-known existing anonymity measures.

Justin Thaler, Mike Roberts, Michael Mitzenmacher et al.

As the cloud computing paradigm has gained prominence, the need for verifiable computation has grown increasingly urgent. The concept of verifiable computation enables a weak client to outsource difficult computations to a powerful, but untrusted, server. Protocols for verifiable computation aim to provide the client with a guarantee that the server performed the requested computations correctly, without requiring the client to perform the computations herself. By design, these protocols impose a minimal computational burden on the client. However, existing protocols require the server to perform a large amount of extra bookkeeping in order to enable a client to easily verify the results. Verifiable computation has thus remained a theoretical curiosity, and protocols for it have not been implemented in real cloud computing systems. Our goal is to leverage GPUs to reduce the server-side slowdown for verifiable computation. To this end, we identify abundant data parallelism in a state-of-the-art general-purpose protocol for verifiable computation, originally due to Goldwasser, Kalai, and Rothblum, and recently extended by Cormode, Mitzenmacher, and Thaler. We implement this protocol on the GPU, obtaining 40-120x server-side speedups relative to a state-of-the-art sequential implementation. For benchmark problems, our implementation reduces the slowdown of the server to factors of 100-500x relative to the original computations requested by the client. Furthermore, we reduce the already small runtime of the client by 100x. Similarly, we obtain 20-50x server-side and client-side speedups for related protocols targeted at specific streaming problems. We believe our results demonstrate the immediate practicality of using GPUs for verifiable computation, and more generally that protocols for verifiable computation have become sufficiently mature to deploy in real cloud computing systems.