Faster Maximum Inner Product Search in High Dimensions

Maximum Inner Product Search (MIPS) is a ubiquitous task in machine learning applications such as recommendation systems. Given a query vector and $n$ atom vectors in $d$-dimensional space, the goal of MIPS is to find the atom that has the highest inner product with the query vector. Existing MIPS algorithms scale at least as $O(\sqrt{d})$, which becomes computationally prohibitive in high-dimensional settings. In this work, we present BanditMIPS, a novel randomized MIPS algorithm whose complexity is independent of $d$. BanditMIPS estimates the inner product for each atom by subsampling coordinates and adaptively evaluates more coordinates for more promising atoms. The specific adaptive sampling strategy is motivated by multi-armed bandits. We provide theoretical guarantees that BanditMIPS returns the correct answer with high probability, while improving the complexity in $d$ from $O(\sqrt{d})$ to $O(1)$. We also perform experiments on four synthetic and real-world datasets and demonstrate that BanditMIPS outperforms prior state-of-the-art algorithms. For example, in the Movie Lens dataset ($n$=4,000, $d$=6,000), BanditMIPS is 20$\times$ faster than the next best algorithm while returning the same answer. BanditMIPS requires no preprocessing of the data and includes a hyperparameter that practitioners may use to trade off accuracy and runtime. We also propose a variant of our algorithm, named BanditMIPS-$\alpha$, which achieves further speedups by employing non-uniform sampling across coordinates. Finally, we demonstrate how known preprocessing techniques can be used to further accelerate BanditMIPS, and discuss applications to Matching Pursuit and Fourier analysis.Comment: 23 page

Impact of geogenic degassing on C-isotopic composition of dissolved carbon in karst systems of Greece

The Earth C-cycle is complex, where endogenic and exogenic sources are interconnected, operating in a multiple spatial and temporal scale (Lee et al., 2019). Non-volcanic CO2 degassing from active tectonic structures is one of the less defined components of this cycle (Frondini et al., 2019). Carbon mass-balance (Chiodini et al., 2000) is a useful tool to quantify the geogenic carbon output from regional karst hydrosystems. This approach has been demonstrated for central Italy and may be valid also for Greece, due to the similar geodynamic settings. Deep degassing in Greece has been ascertained mainly at hydrothermal and volcanic areas, but the impact of geogenic CO2 released by active tectonic areas has not yet been quantified. The main aim of this research is to investigate the possible deep degassing through the big karst aquifers of Greece. Since 2016, 156 karst springs were sampled along most of the Greek territory. To discriminate the sources of carbon, the analysis of the isotopic composition of carbon was carried out. δ13CTDIC values vary from -16.61 to -0.91‰ and can be subdivided into two groups characterized by (a) low δ13CTDIC, and (b) intermediate to high δ13CTDIC with a threshold value of -6.55‰. The composition of the first group can be related to the mixing of organic-derived CO2 and the dissolution of marine carbonates. Springs of the second group, mostly located close to Quaternary volcanic areas, are linked to possible carbon input from deep sources