From 81d386ef3e3bd68a30000b92a19de9676a0ec828 Mon Sep 17 00:00:00 2001
From: Yifan Yang <64255737+yfyeung@users.noreply.github.com>
Date: Thu, 20 Apr 2023 12:27:43 +0800
Subject: [PATCH] Add compute_ppl.py and ngram_entropy_pruning.py (#1013)

---
 .../compute_ppl.py                            | 109 +++
 icefall/shared/ngram_entropy_pruning.py       | 630 ++++++++++++++++++
 2 files changed, 739 insertions(+)
 create mode 100755 egs/gigaspeech/ASR/pruned_transducer_stateless2/compute_ppl.py
 create mode 100755 icefall/shared/ngram_entropy_pruning.py

diff --git a/egs/gigaspeech/ASR/pruned_transducer_stateless2/compute_ppl.py b/egs/gigaspeech/ASR/pruned_transducer_stateless2/compute_ppl.py
new file mode 100755
index 000000000..76306fc4c
--- /dev/null
+++ b/egs/gigaspeech/ASR/pruned_transducer_stateless2/compute_ppl.py
@@ -0,0 +1,109 @@
+#!/usr/bin/env python3
+#
+# Copyright 2023 Xiaomi Corp. (Author: Yifan Yang)
+#
+# See ../../../../LICENSE for clarification regarding multiple authors
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""
+Usage:
+./pruned_transducer_stateless7/compute_ppl.py \
+    --ngram-lm-path ./download/lm/3gram_pruned_1e7.arpa
+
+"""
+
+
+import argparse
+import logging
+import math
+from typing import Dict, List, Optional, Tuple
+
+import kenlm
+import torch
+from asr_datamodule import GigaSpeechAsrDataModule
+
+
+def get_parser():
+    parser = argparse.ArgumentParser(
+        formatter_class=argparse.ArgumentDefaultsHelpFormatter
+    )
+
+    parser.add_argument(
+        "--ngram-lm-path",
+        type=str,
+        default="download/lm/3gram_pruned_1e7.arpa",
+        help="The lang dir containing word table and LG graph",
+    )
+
+    return parser
+
+
+def decode_dataset(
+    dl: torch.utils.data.DataLoader,
+    model: kenlm.Model,
+) -> Dict[str, float]:
+    """
+    Args:
+      dl:
+        PyTorch's dataloader containing the dataset to decode.
+      model:
+        A ngram lm of kenlm.Model object.
+    Returns:
+      Return the perplexity of the giving dataset.
+    """
+    sum_score_log = 0
+    sum_n = 0
+    for batch_idx, batch in enumerate(dl):
+        texts = batch["supervisions"]["text"]
+        for text in texts:
+            sum_n += len(text.split()) + 1
+            sum_score_log += -1 * model.score(text)
+
+    ppl = math.pow(10.0, sum_score_log / sum_n)
+
+    return ppl
+
+
+def main():
+    parser = get_parser()
+    GigaSpeechAsrDataModule.add_arguments(parser)
+    args = parser.parse_args()
+
+    logging.info("About to load ngram LM")
+    model = kenlm.Model(args.ngram_lm_path)
+
+    gigaspeech = GigaSpeechAsrDataModule(args)
+
+    dev_cuts = gigaspeech.dev_cuts()
+    test_cuts = gigaspeech.test_cuts()
+
+    dev_dl = gigaspeech.test_dataloaders(dev_cuts)
+    test_dl = gigaspeech.test_dataloaders(test_cuts)
+
+    test_sets = ["dev", "test"]
+    test_dls = [dev_dl, test_dl]
+
+    for test_set, test_dl in zip(test_sets, test_dls):
+        ppl = decode_dataset(
+            dl=test_dl,
+            model=model,
+        )
+        logging.info(f"{test_set} PPL: {ppl}")
+
+    logging.info("Done!")
+
+
+if __name__ == "__main__":
+    formatter = "%(asctime)s %(levelname)s [%(filename)s:%(lineno)d] %(message)s"
+    logging.basicConfig(format=formatter, level=logging.INFO)
+    main()
diff --git a/icefall/shared/ngram_entropy_pruning.py b/icefall/shared/ngram_entropy_pruning.py
new file mode 100755
index 000000000..b1ebee9ea
--- /dev/null
+++ b/icefall/shared/ngram_entropy_pruning.py
@@ -0,0 +1,630 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+#
+# Copyright 2021  Johns Hopkins University (Author: Ruizhe Huang)
+#
+# See ../../../../LICENSE for clarification regarding multiple authors
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""
+Usage:
+./ngram_entropy_pruning.py \
+    -threshold 1e-8 \
+    -lm download/lm/4gram.arpa \
+    -write-lm download/lm/4gram_pruned_1e8.arpa
+
+This file is from Kaldi `egs/wsj/s5/utils/lang/ngram_entropy_pruning.py`.
+This is an implementation of ``Entropy-based Pruning of Backoff Language Models''
+in the same way as SRILM.
+"""
+
+
+import argparse
+import gzip
+import logging
+import math
+import re
+from collections import OrderedDict, defaultdict
+from enum import Enum, unique
+from io import StringIO
+
+parser = argparse.ArgumentParser(
+    description="""
+    Prune an n-gram language model based on the relative entropy 
+    between the original and the pruned model, based on Andreas Stolcke's paper.
+    An n-gram entry is removed, if the removal causes (training set) perplexity 
+    of the model to increase by less than threshold relative.
+    
+    The command takes an arpa file and a pruning threshold as input, 
+    and outputs a pruned arpa file.
+    """
+)
+parser.add_argument("-threshold", type=float, default=1e-6, help="Order of n-gram")
+parser.add_argument("-lm", type=str, default=None, help="Path to the input arpa file")
+parser.add_argument(
+    "-write-lm", type=str, default=None, help="Path to output arpa file after pruning"
+)
+parser.add_argument(
+    "-minorder",
+    type=int,
+    default=1,
+    help="The minorder parameter limits pruning to ngrams of that length and above.",
+)
+parser.add_argument(
+    "-encoding", type=str, default="utf-8", help="Encoding of the arpa file"
+)
+parser.add_argument(
+    "-verbose",
+    type=int,
+    default=2,
+    choices=[0, 1, 2, 3, 4, 5],
+    help="Verbose level, where 0 is most noisy; 5 is most silent",
+)
+args = parser.parse_args()
+
+default_encoding = args.encoding
+logging.basicConfig(
+    format="%(asctime)s — %(levelname)s — %(funcName)s:%(lineno)d — %(message)s",
+    level=args.verbose * 10,
+)
+
+
+class Context(dict):
+    """
+    This class stores data for a context h.
+    It behaves like a python dict object, except that it has several
+    additional attributes.
+    """
+
+    def __init__(self):
+        super().__init__()
+        self.log_bo = None
+
+
+class Arpa:
+    """
+    This is a class that implement the data structure of an APRA LM.
+    It (as well as some other classes) is modified based on the library
+    by Stefan Fischer:
+    https://github.com/sfischer13/python-arpa
+    """
+
+    UNK = "<unk>"
+    SOS = "<s>"
+    EOS = "</s>"
+    FLOAT_NDIGITS = 7
+    base = 10
+
+    @staticmethod
+    def _check_input(my_input):
+        if not my_input:
+            raise ValueError
+        elif isinstance(my_input, tuple):
+            return my_input
+        elif isinstance(my_input, list):
+            return tuple(my_input)
+        elif isinstance(my_input, str):
+            return tuple(my_input.strip().split(" "))
+        else:
+            raise ValueError
+
+    @staticmethod
+    def _check_word(input_word):
+        if not isinstance(input_word, str):
+            raise ValueError
+        if " " in input_word:
+            raise ValueError
+
+    def _replace_unks(self, words):
+        return tuple((w if w in self else self._unk) for w in words)
+
+    def __init__(self, path=None, encoding=None, unk=None):
+        self._counts = OrderedDict()
+        self._ngrams = (
+            OrderedDict()
+        )  # Use self._ngrams[len(h)][h][w] for saving the entry of (h,w)
+        self._vocabulary = set()
+        if unk is None:
+            self._unk = self.UNK
+
+        if path is not None:
+            self.loadf(path, encoding)
+
+    def __contains__(self, ngram):
+        h = ngram[:-1]  # h is a tuple
+        w = ngram[-1]  # w is a string/word
+        return h in self._ngrams[len(h)] and w in self._ngrams[len(h)][h]
+
+    def contains_word(self, word):
+        self._check_word(word)
+        return word in self._vocabulary
+
+    def add_count(self, order, count):
+        self._counts[order] = count
+        self._ngrams[order - 1] = defaultdict(Context)
+
+    def update_counts(self):
+        for order in range(1, self.order() + 1):
+            count = sum([len(wlist) for _, wlist in self._ngrams[order - 1].items()])
+            if count > 0:
+                self._counts[order] = count
+
+    def add_entry(self, ngram, p, bo=None, order=None):
+        # Note: ngram is a tuple of strings, e.g. ("w1", "w2", "w3")
+        h = ngram[:-1]  # h is a tuple
+        w = ngram[-1]  # w is a string/word
+
+        # Note that p and bo here are in fact in the log domain (self.base = 10)
+        h_context = self._ngrams[len(h)][h]
+        h_context[w] = p
+        if bo is not None:
+            self._ngrams[len(ngram)][ngram].log_bo = bo
+
+        for word in ngram:
+            self._vocabulary.add(word)
+
+    def counts(self):
+        return sorted(self._counts.items())
+
+    def order(self):
+        return max(self._counts.keys(), default=None)
+
+    def vocabulary(self, sort=True):
+        if sort:
+            return sorted(self._vocabulary)
+        else:
+            return self._vocabulary
+
+    def _entries(self, order):
+        return (
+            self._entry(h, w)
+            for h, wlist in self._ngrams[order - 1].items()
+            for w in wlist
+        )
+
+    def _entry(self, h, w):
+        # return the entry for the ngram (h, w)
+        ngram = h + (w,)
+        log_p = self._ngrams[len(h)][h][w]
+        log_bo = self._log_bo(ngram)
+        if log_bo is not None:
+            return (
+                round(log_p, self.FLOAT_NDIGITS),
+                ngram,
+                round(log_bo, self.FLOAT_NDIGITS),
+            )
+        else:
+            return round(log_p, self.FLOAT_NDIGITS), ngram
+
+    def _log_bo(self, ngram):
+        if len(ngram) in self._ngrams and ngram in self._ngrams[len(ngram)]:
+            return self._ngrams[len(ngram)][ngram].log_bo
+        else:
+            return None
+
+    def _log_p(self, ngram):
+        h = ngram[:-1]  # h is a tuple
+        w = ngram[-1]  # w is a string/word
+        if h in self._ngrams[len(h)] and w in self._ngrams[len(h)][h]:
+            return self._ngrams[len(h)][h][w]
+        else:
+            return None
+
+    def log_p_raw(self, ngram):
+        log_p = self._log_p(ngram)
+        if log_p is not None:
+            return log_p
+        else:
+            if len(ngram) == 1:
+                raise KeyError
+            else:
+                log_bo = self._log_bo(ngram[:-1])
+                if log_bo is None:
+                    log_bo = 0
+                return log_bo + self.log_p_raw(ngram[1:])
+
+    def log_joint_prob(self, sequence):
+        # Compute the joint prob of the sequence based on the chain rule
+        # Note that sequence should be a tuple of strings
+        #
+        # Reference:
+        # https://github.com/BitSpeech/SRILM/blob/d571a4424fb0cf08b29fbfccfddd092ea969eae3/lm/src/LM.cc#L527
+
+        log_joint_p = 0
+        seq = sequence
+        while len(seq) > 0:
+            log_joint_p += self.log_p_raw(seq)
+            seq = seq[:-1]
+
+            # If we're computing the marginal probability of the unigram
+            # <s> context we have to look up </s> instead since the former
+            # has prob = 0.
+            if len(seq) == 1 and seq[0] == self.SOS:
+                seq = (self.EOS,)
+
+        return log_joint_p
+
+    def set_new_context(self, h):
+        old_context = self._ngrams[len(h)][h]
+        self._ngrams[len(h)][h] = Context()
+        return old_context
+
+    def log_p(self, ngram):
+        words = self._check_input(ngram)
+        if self._unk:
+            words = self._replace_unks(words)
+        return self.log_p_raw(words)
+
+    def log_s(self, sentence, sos=SOS, eos=EOS):
+        words = self._check_input(sentence)
+        if self._unk:
+            words = self._replace_unks(words)
+        if sos:
+            words = (sos,) + words
+        if eos:
+            words = words + (eos,)
+        result = sum(self.log_p_raw(words[:i]) for i in range(1, len(words) + 1))
+        if sos:
+            result = result - self.log_p_raw(words[:1])
+        return result
+
+    def p(self, ngram):
+        return self.base ** self.log_p(ngram)
+
+    def s(self, sentence):
+        return self.base ** self.log_s(sentence)
+
+    def write(self, fp):
+        fp.write("\n\\data\\\n")
+        for order, count in self.counts():
+            fp.write("ngram {}={}\n".format(order, count))
+        fp.write("\n")
+        for order, _ in self.counts():
+            fp.write("\\{}-grams:\n".format(order))
+            for e in self._entries(order):
+                prob = e[0]
+                ngram = " ".join(e[1])
+                if len(e) == 2:
+                    fp.write("{}\t{}\n".format(prob, ngram))
+                elif len(e) == 3:
+                    backoff = e[2]
+                    fp.write("{}\t{}\t{}\n".format(prob, ngram, backoff))
+                else:
+                    raise ValueError
+            fp.write("\n")
+        fp.write("\\end\\\n")
+
+
+class ArpaParser:
+    """
+    This is a class that implement a parser of an arpa file
+    """
+
+    @unique
+    class State(Enum):
+        DATA = 1
+        COUNT = 2
+        HEADER = 3
+        ENTRY = 4
+
+    re_count = re.compile(r"^ngram (\d+)=(\d+)$")
+    re_header = re.compile(r"^\\(\d+)-grams:$")
+    re_entry = re.compile(
+        "^(-?\\d+(\\.\\d+)?([eE]-?\\d+)?)"
+        "\t"
+        "(\\S+( \\S+)*)"
+        "(\t((-?\\d+(\\.\\d+)?)([eE]-?\\d+)?))?$"
+    )
+
+    def _parse(self, fp):
+        self._result = []
+        self._state = self.State.DATA
+        self._tmp_model = None
+        self._tmp_order = None
+        for line in fp:
+            line = line.strip()
+            if self._state == self.State.DATA:
+                self._data(line)
+            elif self._state == self.State.COUNT:
+                self._count(line)
+            elif self._state == self.State.HEADER:
+                self._header(line)
+            elif self._state == self.State.ENTRY:
+                self._entry(line)
+        if self._state != self.State.DATA:
+            raise Exception(line)
+        return self._result
+
+    def _data(self, line):
+        if line == "\\data\\":
+            self._state = self.State.COUNT
+            self._tmp_model = Arpa()
+        else:
+            pass  # skip comment line
+
+    def _count(self, line):
+        match = self.re_count.match(line)
+        if match:
+            order = match.group(1)
+            count = match.group(2)
+            self._tmp_model.add_count(int(order), int(count))
+        elif not line:
+            self._state = self.State.HEADER  # there are no counts
+        else:
+            raise Exception(line)
+
+    def _header(self, line):
+        match = self.re_header.match(line)
+        if match:
+            self._state = self.State.ENTRY
+            self._tmp_order = int(match.group(1))
+        elif line == "\\end\\":
+            self._result.append(self._tmp_model)
+            self._state = self.State.DATA
+            self._tmp_model = None
+            self._tmp_order = None
+        elif not line:
+            pass  # skip empty line
+        else:
+            raise Exception(line)
+
+    def _entry(self, line):
+        match = self.re_entry.match(line)
+        if match:
+            p = self._float_or_int(match.group(1))
+            ngram = tuple(match.group(4).split(" "))
+            bo_match = match.group(7)
+            bo = self._float_or_int(bo_match) if bo_match else None
+            self._tmp_model.add_entry(ngram, p, bo, self._tmp_order)
+        elif not line:
+            self._state = self.State.HEADER  # last entry
+        else:
+            raise Exception(line)
+
+    @staticmethod
+    def _float_or_int(s):
+        f = float(s)
+        i = int(f)
+        if str(i) == s:  # don't drop trailing ".0"
+            return i
+        else:
+            return f
+
+    def load(self, fp):
+        """Deserialize fp (a file-like object) to a Python object."""
+        return self._parse(fp)
+
+    def loadf(self, path, encoding=None):
+        """Deserialize path (.arpa, .gz) to a Python object."""
+        path = str(path)
+        if path.endswith(".gz"):
+            with gzip.open(path, mode="rt", encoding=encoding) as f:
+                return self.load(f)
+        else:
+            with open(path, mode="rt", encoding=encoding) as f:
+                return self.load(f)
+
+    def loads(self, s):
+        """Deserialize s (a str) to a Python object."""
+        with StringIO(s) as f:
+            return self.load(f)
+
+    def dump(self, obj, fp):
+        """Serialize obj to fp (a file-like object) in ARPA format."""
+        obj.write(fp)
+
+    def dumpf(self, obj, path, encoding=None):
+        """Serialize obj to path in ARPA format (.arpa, .gz)."""
+        path = str(path)
+        if path.endswith(".gz"):
+            with gzip.open(path, mode="wt", encoding=encoding) as f:
+                return self.dump(obj, f)
+        else:
+            with open(path, mode="wt", encoding=encoding) as f:
+                self.dump(obj, f)
+
+    def dumps(self, obj):
+        """Serialize obj to an ARPA formatted str."""
+        with StringIO() as f:
+            self.dump(obj, f)
+            return f.getvalue()
+
+
+def add_log_p(prev_log_sum, log_p, base):
+    return math.log(base**log_p + base**prev_log_sum, base)
+
+
+def compute_numerator_denominator(lm, h):
+    log_sum_seen_h = -math.inf
+    log_sum_seen_h_lower = -math.inf
+    base = lm.base
+    for w, log_p in lm._ngrams[len(h)][h].items():
+        log_sum_seen_h = add_log_p(log_sum_seen_h, log_p, base)
+
+        ngram = h + (w,)
+        log_p_lower = lm.log_p_raw(ngram[1:])
+        log_sum_seen_h_lower = add_log_p(log_sum_seen_h_lower, log_p_lower, base)
+
+    numerator = 1.0 - base**log_sum_seen_h
+    denominator = 1.0 - base**log_sum_seen_h_lower
+    return numerator, denominator
+
+
+def prune(lm, threshold, minorder):
+    # Reference:
+    # https://github.com/BitSpeech/SRILM/blob/d571a4424fb0cf08b29fbfccfddd092ea969eae3/lm/src/NgramLM.cc#L2330
+
+    for i in range(
+        lm.order(), max(minorder - 1, 1), -1
+    ):  # i is the order of the ngram (h, w)
+        logging.info("processing %d-grams ..." % i)
+        count_pruned_ngrams = 0
+
+        h_dict = lm._ngrams[i - 1]
+        for h in list(h_dict.keys()):
+            # old backoff weight, BOW(h)
+            log_bow = lm._log_bo(h)
+            if log_bow is None:
+                log_bow = 0
+
+            # Compute numerator and denominator of the backoff weight,
+            # so that we can quickly compute the BOW adjustment due to
+            # leaving out one prob.
+            numerator, denominator = compute_numerator_denominator(lm, h)
+
+            # assert abs(math.log(numerator, lm.base) - math.log(denominator, lm.base) - h_dict[h].log_bo) < 1e-5
+
+            # Compute the marginal probability of the context, P(h)
+            h_log_p = lm.log_joint_prob(h)
+
+            all_pruned = True
+            pruned_w_set = set()
+
+            for w, log_p in h_dict[h].items():
+                ngram = h + (w,)
+
+                # lower-order estimate for ngramProb, P(w|h')
+                backoff_prob = lm.log_p_raw(ngram[1:])
+
+                # Compute BOW after removing ngram, BOW'(h)
+                new_log_bow = math.log(
+                    numerator + lm.base**log_p, lm.base
+                ) - math.log(denominator + lm.base**backoff_prob, lm.base)
+
+                # Compute change in entropy due to removal of ngram
+                delta_prob = backoff_prob + new_log_bow - log_p
+                delta_entropy = -(lm.base**h_log_p) * (
+                    (lm.base**log_p) * delta_prob
+                    + numerator * (new_log_bow - log_bow)
+                )
+
+                # compute relative change in model (training set) perplexity
+                perp_change = lm.base**delta_entropy - 1.0
+
+                pruned = threshold > 0 and perp_change < threshold
+
+                # Make sure we don't prune ngrams whose backoff nodes are needed
+                if (
+                    pruned
+                    and len(ngram) in lm._ngrams
+                    and len(lm._ngrams[len(ngram)][ngram]) > 0
+                ):
+                    pruned = False
+
+                logging.debug(
+                    "CONTEXT "
+                    + str(h)
+                    + " WORD "
+                    + w
+                    + " CONTEXTPROB %f " % h_log_p
+                    + " OLDPROB %f " % log_p
+                    + " NEWPROB %f " % (backoff_prob + new_log_bow)
+                    + " DELTA-H %f " % delta_entropy
+                    + " DELTA-LOGP %f " % delta_prob
+                    + " PPL-CHANGE %f " % perp_change
+                    + " PRUNED "
+                    + str(pruned)
+                )
+
+                if pruned:
+                    pruned_w_set.add(w)
+                    count_pruned_ngrams += 1
+                else:
+                    all_pruned = False
+
+            # If we removed all ngrams for this context we can
+            # remove the context itself, but only if the present
+            # context is not a prefix to a longer one.
+            if all_pruned and len(pruned_w_set) == len(h_dict[h]):
+                del h_dict[
+                    h
+                ]  # this context h is no longer needed, as its ngram prob is stored at its own context h'
+            elif len(pruned_w_set) > 0:
+                # The pruning for this context h is actually done here
+                old_context = lm.set_new_context(h)
+
+                for w, p_w in old_context.items():
+                    if w not in pruned_w_set:
+                        lm.add_entry(
+                            h + (w,), p_w
+                        )  # the entry hw is stored at the context h
+
+                # We need to recompute the back-off weight, but
+                # this can only be done after completing the pruning
+                # of the lower-order ngrams.
+                # Reference:
+                # https://github.com/BitSpeech/SRILM/blob/d571a4424fb0cf08b29fbfccfddd092ea969eae3/flm/src/FNgramLM.cc#L2124
+
+        logging.info("pruned %d %d-grams" % (count_pruned_ngrams, i))
+
+    # recompute backoff weights
+    for i in range(
+        max(minorder - 1, 1) + 1, lm.order() + 1
+    ):  # be careful of this order: from low- to high-order
+        for h in lm._ngrams[i - 1]:
+            numerator, denominator = compute_numerator_denominator(lm, h)
+            new_log_bow = math.log(numerator, lm.base) - math.log(denominator, lm.base)
+            lm._ngrams[len(h)][h].log_bo = new_log_bow
+
+    # update counts
+    lm.update_counts()
+
+    return
+
+
+def check_h_is_valid(lm, h):
+    sum_under_h = sum(
+        [lm.base ** lm.log_p_raw(h + (w,)) for w in lm.vocabulary(sort=False)]
+    )
+    if abs(sum_under_h - 1.0) > 1e-6:
+        logging.info("warning: %s %f" % (str(h), sum_under_h))
+        return False
+    else:
+        return True
+
+
+def validate_lm(lm):
+    # sanity check if the conditional probability sums to one under each context h
+    for i in range(lm.order(), 0, -1):  # i is the order of the ngram (h, w)
+        logging.info("validating %d-grams ..." % i)
+        h_dict = lm._ngrams[i - 1]
+        for h in h_dict.keys():
+            check_h_is_valid(lm, h)
+
+
+def compare_two_apras(path1, path2):
+    pass
+
+
+if __name__ == "__main__":
+    # load an arpa file
+    logging.info("Loading the arpa file from %s" % args.lm)
+    parser = ArpaParser()
+    models = parser.loadf(args.lm, encoding=default_encoding)
+    lm = models[0]  # ARPA files may contain several models.
+    logging.info("Stats before pruning:")
+    for i, cnt in lm.counts():
+        logging.info("ngram %d=%d" % (i, cnt))
+
+    # prune it, the language model will be modified in-place
+    logging.info("Start pruning the model with threshold=%.3E..." % args.threshold)
+    prune(lm, args.threshold, args.minorder)
+
+    # validate_lm(lm)
+
+    # write the arpa language model to a file
+    logging.info("Stats after pruning:")
+    for i, cnt in lm.counts():
+        logging.info("ngram %d=%d" % (i, cnt))
+    logging.info("Saving the pruned arpa file to %s" % args.write_lm)
+    parser.dumpf(lm, args.write_lm, encoding=default_encoding)
+    logging.info("Done.")