Current state of the art methods for generating Pareto-optimal solutions for multi-objective optimization problems mostly rely on optimizing the hyper-parameters of the models (HPO - hyper-parameter Optimization). Few recent, less studied methods focus on optimizing over the space of model parameters, leveraging the problem specific knowledge. We present a generic first-of-a-kind method, referred to as HyperASPO, that combines optimization over the spaces of both hyper-parameters and model parameters for multi-objective optimization of learning problems. HyperASPO consists of two stages. First, we perform a coarse HPO to determine a set of favorable hyper-parameter configurations. In the second step, for each of these configurations, we solve a sequence of weighted single objective optimization problems for estimating Pareto-optimal solutions. We generate the weights in the second step using an adaptive mesh constructed iteratively based on the metrics of interest, resulting in further refinement of Pareto frontier efficiently. We consider the widely used XGBoost (Gradient Boosted Trees) model and validate our method on multiple classification datasets. Our proposed method shows up to 20% improvement over the hypervolumes of Pareto fronts obtained through state of the art HPO based methods with up to 2× reduction in computational time.

The cost of decompressing (decoding) data can be prohibitive for certain real-time applications. In many scenarios, it is acceptable to sacrifice (to some extent) on compression in the interest of fast decoding. We study anovel problem of finding a prefix tree having the best decode time under the constraint that the code length does not exceed a certain threshold for a natural class of memory access cost functions that use blocking (also referred to as lookup tables). We present exact and approximation algorithms for this problem that are based on dynamic programming and capitalize on interesting structures of the optimal solutions. The full version of this paper is available at [1]

The cost of uncompressing (decoding) data can be prohibitive in certain real-time applications, for example when predicting using compressed deep learning models. In many scenarios, it is acceptable to sacrifice to some extent on compression in the interest of fast decoding. In this work, we are interested in finding the prefix tree having the best decode time under the constraint that the code length does not exceed a certain threshold for a natural class of algorithms under the hierarchical memory model. We present an efficient optimal algorithm for this problem based on a dynamic program that capitalizes on an interesting structure of the optimal solution.

In this paper, we present a comprehensive theoretical analysis of the sampling technique for the association rule mining problem. Most of the previous works have concentrated only on the empirical evaluation of the effectiveness of sampling for the step of finding frequent itemsets. To the best of our knowledge, a theoretical framework to analyze the quality of the solutions obtained by sampling has not been studied. Our contributions are two-fold. First, we present the notions of ε-close frequent itemset mining and ε-close association rule mining that help assess the quality of the solutions obtained by sampling. Secondly, we show that both the frequent items mining and association rule mining problems can be solved satisfactorily with a sample size that is independent of both the number of transactions size and the number of items. Let θ be the required support, ε the closeness parameter, and 1/h the desired bound on the probability of failure. We show that the sampling based analysis succeeds in solving both ε-close frequent itemset mining and ε-close association rule mining with a probability of at least (1 - 1/h) with a sample of size S = O(1/ε2θ [Δ + log h/(1 - ε)θ]), where Δ is the maximum number of items present in any transaction. Thus, we establish that it is possible to speed up the entire process of association rule mining for massive databases by working with a small sample while retaining any desired degree of accuracy. Our work gives a comprehensive explanation for the well known empirical successes of sampling for association rule mining.